第三周补着写一下，最近确实太忙了，数据库课设，专业实习，一堆东西忙着搞不完，说好的暑假好好学算法呢，呜呜我的时间去哪里了

题面一堆Yuki，是的没错孩子们这场是我出的（x

F Flower

签到。先判无解情况，然后把n分成若干(a+b)整段，剩余的部分小于等于a就是要去掉的花瓣，否则不操作。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
/*

This code template was updated by Yukii_P on 2025/4/4.

*/
#include <bits/stdc++.h>
#define FIO cin.tie(0); ios::sync_with_stdio(false)
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define TEST
#define TESTS int t = 1; cin >> t; while (t--)

#if 0
#define int i64
#define inf 0x3f3f3f3f3f3f3f3fLL
#else
#define inf 0x3f3f3f3f
#endif

#ifndef ONLINE_JUDGE
#define debug(...) std::cerr << #__VA_ARGS__ << " = "; dbg1(__VA_ARGS__)
void dbg2() { std::cerr << "\n"; }
template<typename T, typename... T2>
void dbg2(T x, T2... args) {
    std::cerr << ", " << x;
    dbg2(args...);
}
template<typename T, typename... T2>
void dbg1(T x, T2... args) {
    std::cerr << x;
    dbg2(args...);
}
#else
#define debug(...) 
#endif

using namespace std;
using i64 = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using pii = std::pair<int, int>;

inline char nc() {
    static char buf[1 << 20], *p1, *p2;
    return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 20, stdin), p1 == p2) ? EOF : *p1++;
}
#ifndef ONLINE_JUDGE
#define nc getchar
#endif
void read() {}
template<typename T, typename... T2> 
inline void read(T &x, T2 &... oth) {
    x = 0; char c = nc(), up = c;
    while(!isdigit(c)) up = c, c = nc();
    while(isdigit(c)) x = x * 10 + c - '0', c = nc();
    up == '-' ? x = -x : 0;
    read(oth...);
}

constexpr int N = 2e5 + 10;
constexpr int MOD = 998244353;

void solve() {
    i64 n, a, b;
    cin >> n >> a >> b;
    if (n <= a) {
        cout << "Sayonara\n";
        return;
    }
    if (n % (a + b) <= a) {
        cout << (n % (a + b)) << "\n";
    } else {
        cout << 0 << "\n";
    }
}

signed main() {
    
    FIO;
    TESTS {
        solve();
    }

    return 0;
}

/*

  _  _                            _____             _               _               _    
 | \| |    ___    _ _      ___   |_   _|    _ _    (_)    __ __    (_)    __ _     | |   
 | .` |   / _ \  | ' \    |___|    | |     | '_|   | |    \ V /    | |   / _` |    | |   
 |_|\_|   \___/  |_||_|   _____   _|_|_   _|_|_   _|_|_   _\_/_   _|_|_  \__,_|   _|_|_  
_|"""""|_|"""""|_|"""""|_|     |_|"""""|_|"""""|_|"""""|_|"""""|_|"""""|_|"""""|_|"""""| 
"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-' 

(Font: ASCII - Train)

"El Psy Kongroo." -- Hououin Kyoma

"私は極色カスタ推しです...だが、狽音ウルシと夜鳴トバリも推す :)" -- Yukii_P

*/

J Jetton

思洋写的，还没看。有空一定看。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
#include<bits/stdc++.h>

using namespace std;

using ll = long long;
using ull = unsigned long long;
using i32 = int;
using i64 = long long;
using i128 = __int128;

template<typename T1,typename T2>
ostream& operator<<(ostream& o,const tuple<T1,T2>& t){
	return o<<"("<<get<0>(t)<<","<<get<1>(t)<<")";
}

template<typename T1,typename T2,typename T3>
ostream& operator<<(ostream& o,const tuple<T1,T2,T3>& t){
	return o<<"("<<get<0>(t)<<","<<get<1>(t)<<","<<get<2>(t)<<")";
}

template<typename T>
ostream& operator<<(ostream& o,const vector<T>& vec){
	for(int i=(o<<"[",0);i<vec.size();++i)o<<vec[i]<<",]"[i==vec.size()-1];
	return o<<"\n";
}

constexpr int M = 2e5+5, mod = 1e9+7;// 998244353;
constexpr double pi = acos(-1), eps = 1e-9;

void solve(){
	int x,y;
	cin>>x>>y;
	if(x==y){
		cout<<"1\n";
		return;
	}
	ll t=(x+y)/gcd(x,y);
	if(t!=(t&-t)){
		cout<<"-1\n";
		return;
	}
	for(int i=1;i<32;++i){
		if((t>>i)&1){
			cout<<i<<"\n";
			return;
		}
	}
	
	return;
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	
	int t{1};
	cin>>t;
	while(t--){
		solve();
	}
	
	return 0;
}

D Distant Control

没想清楚就写导致的。WA了一堆。下次先给老子把性质分析清楚再写————

如果存在长度不少于a+1的连续0串或长度不少于a的连续1串结果就是全部开启，否则就是1的数量。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
/*

This code template was updated by Yukii_P on 2025/4/4.

*/
#include <bits/stdc++.h>
#define FIO cin.tie(0); ios::sync_with_stdio(false)
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define TEST
#define TESTS int t = 1; cin >> t; while (t--)

#if 0
#define int i64
#define inf 0x3f3f3f3f3f3f3f3fLL
#else
#define inf 0x3f3f3f3f
#endif

#ifndef ONLINE_JUDGE
#define debug(...) std::cerr << #__VA_ARGS__ << " = "; dbg1(__VA_ARGS__)
void dbg2() { std::cerr << "\n"; }
template<typename T, typename... T2>
void dbg2(T x, T2... args) {
    std::cerr << ", " << x;
    dbg2(args...);
}
template<typename T, typename... T2>
void dbg1(T x, T2... args) {
    std::cerr << x;
    dbg2(args...);
}
#else
#define debug(...) 
#endif

using namespace std;
using i64 = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using pii = std::pair<int, int>;

inline char nc() {
    static char buf[1 << 20], *p1, *p2;
    return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 20, stdin), p1 == p2) ? EOF : *p1++;
}
#ifndef ONLINE_JUDGE
#define nc getchar
#endif
void read() {}
template<typename T, typename... T2> 
inline void read(T &x, T2 &... oth) {
    x = 0; char c = nc(), up = c;
    while(!isdigit(c)) up = c, c = nc();
    while(isdigit(c)) x = x * 10 + c - '0', c = nc();
    up == '-' ? x = -x : 0;
    read(oth...);
}

constexpr int N = 2e5 + 10;
constexpr int MOD = 998244353;

void solve() {
    int n, a;
    cin >> n >> a;
    string s;
    cin >> s;
    int c0 = 0, c1 = 0;
    int ans = 0;
    int ok = 0;
    for (int i = 0; i < n; ++i) {
        char c = s[i];
        if (c == '0') {
            if (i && s[i - 1] == '1') c0 = 0;
            c0++;
        } else {
            if (i && s[i - 1] == '0') c1 = 0;
            c1++;
            ans++;
        }
        if (c0 >= a + 1 || c1 >= a) ok = 1;
    }
    if (ok) {
        cout << n << "\n";
        return;
    }
    cout << ans << "\n";
}

signed main() {
    
    FIO;
    TESTS {
        solve();
    }

    return 0;
}

/*

  _  _                            _____             _               _               _    
 | \| |    ___    _ _      ___   |_   _|    _ _    (_)    __ __    (_)    __ _     | |   
 | .` |   / _ \  | ' \    |___|    | |     | '_|   | |    \ V /    | |   / _` |    | |   
 |_|\_|   \___/  |_||_|   _____   _|_|_   _|_|_   _|_|_   _\_/_   _|_|_  \__,_|   _|_|_  
_|"""""|_|"""""|_|"""""|_|     |_|"""""|_|"""""|_|"""""|_|"""""|_|"""""|_|"""""|_|"""""| 
"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-' 

(Font: ASCII - Train)

"El Psy Kongroo." -- Hououin Kyoma

"私は極色カスタ推しです...だが、狽音ウルシと夜鳴トバリも推す :)" -- Yukii_P

*/

A Ad-hoc Newbie

不会构造。又当躺赢狗了。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
#include<bits/stdc++.h>

using namespace std;

using ll = long long;
using ull = unsigned long long;
using i32 = int;
using i64 = long long;
using i128 = __int128;

template<typename T1,typename T2>
ostream& operator<<(ostream& o,const tuple<T1,T2>& t){
	return o<<"("<<get<0>(t)<<","<<get<1>(t)<<")";
}

template<typename T1,typename T2,typename T3>
ostream& operator<<(ostream& o,const tuple<T1,T2,T3>& t){
	return o<<"("<<get<0>(t)<<","<<get<1>(t)<<","<<get<2>(t)<<")";
}

template<typename T>
ostream& operator<<(ostream& o,const vector<T>& vec){
	for(int i=(o<<"[",0);i<vec.size();++i)o<<vec[i]<<",]"[i==vec.size()-1];
	return o<<"\n";
}

constexpr int M = 2e5+5, mod = 1e9+7;// 998244353;
constexpr double pi = acos(-1), eps = 1e-9;

void solve(){
	int n;
	cin>>n;
	vector<int> f(n);
	vector m(n,vector<int>(n));
	for(int i=0;auto& x:f){
		cin>>x;
		if(x!=1)m[i][i]=1;
		int y=1;
		for(int j=0;j<i;++j){
			if(y&&y+1<x)++y;
			else y=0;
			m[i][j]=m[j][i]=y;
		}
		++i;
	}
	for(auto& i:m){
		for(auto& j:i){
			cout<<j<<" ";
		}
		cout<<"\n";
	}
	
	return;
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	
	int t{1};
	cin>>t;
	while(t--){
		solve();
	}
	
	return 0;
}

E Equal

把每个不同质因子当成独立的维度去考虑。显然n是奇数情况下，无论如何都能进行操作使每个数有相同质因子，必定有解。否则n是偶数，特判n=2，其他情况，记录每个质因子的总数量，如果某个总数量是奇数则无解，否则有解。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
/*

This code template was updated by Yukii_P on 2025/4/4.

*/
#include <bits/stdc++.h>
#include <bits/extc++.h>
#define FIO cin.tie(0); ios::sync_with_stdio(false)
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define TEST
#define TESTS int t = 1; cin >> t; while (t--)

#if 0
#define int i64
#define inf 0x3f3f3f3f3f3f3f3fLL
#else
#define inf 0x3f3f3f3f
#endif

#ifndef ONLINE_JUDGE
#define debug(...) std::cerr << #__VA_ARGS__ << " = "; dbg1(__VA_ARGS__)
void dbg2() { std::cerr << "\n"; }
template<typename T, typename... T2>
void dbg2(T x, T2... args) {
    std::cerr << ", " << x;
    dbg2(args...);
}
template<typename T, typename... T2>
void dbg1(T x, T2... args) {
    std::cerr << x;
    dbg2(args...);
}
#else
#define debug(...) 
#endif

using namespace std;
using namespace __gnu_pbds;
using i64 = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using pii = std::pair<int, int>;

inline char nc() {
    static char buf[1 << 20], *p1, *p2;
    return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 20, stdin), p1 == p2) ? EOF : *p1++;
}
#ifndef ONLINE_JUDGE
#define nc getchar
#endif
void read() {}
template<typename T, typename... T2> 
inline void read(T &x, T2 &... oth) {
    x = 0; char c = nc(), up = c;
    while(!isdigit(c)) up = c, c = nc();
    while(isdigit(c)) x = x * 10 + c - '0', c = nc();
    up == '-' ? x = -x : 0;
    read(oth...);
}

constexpr int N = 5e6 + 10;
constexpr int MOD = 998244353;

int p[N], vis[N], cnt;
void sieve(int n) {
    for (int i = 2; i < n; ++i) {
        if (!vis[i]) p[++cnt] = i;
        for (int j = 1; 1LL * i * p[j] < n; ++j) {
            vis[i * p[j]] = 1;
            if (i % p[j] == 0) break;
        }
    }
    vis[0] = vis[1] = 1;
}

void solve() {
    int n;
    cin >> n;
    vector<int> a(n);
    for (int i = 0; i < n; ++i) cin >> a[i];
    if (n & 1) {
        cout << "YES\n";
        return;
    }
    if (n == 2) {
        cout << (a[0] == a[1] ? "YES" : "NO") << "\n";
        return;
    }
//     unordered_map<int, int> cnt;  // 523ms
    gp_hash_table<int, int> cnt;  // 431ms
//     cc_hash_table<int, int> cnt;  // 467ms
    for (int i = 0; i < n; ++i) {
        if (!vis[a[i]]) {
            cnt[a[i]]++;
            continue;
        }
        for (int j = 1; 1LL * p[j] * p[j] <= a[i]; ++j) {
            int c = 0;
            while (a[i] % p[j] == 0) {
                a[i] /= p[j];
                c++;
            }
            if (c) {
                cnt[p[j]] += c;
            }
            if (!vis[a[i]]) {
                cnt[a[i]]++;
                break;
            }
        }
    }
    for (auto [p, c] : cnt) {
        if (c & 1) {
            cout << "NO\n";
            return;
        }
    }
    cout << "YES\n";
}

signed main() {
    
    FIO;
    sieve(5E6 + 1);
    TESTS {
        solve();
    }

    return 0;
}

/*

  _  _                            _____             _               _               _    
 | \| |    ___    _ _      ___   |_   _|    _ _    (_)    __ __    (_)    __ _     | |   
 | .` |   / _ \  | ' \    |___|    | |     | '_|   | |    \ V /    | |   / _` |    | |   
 |_|\_|   \___/  |_||_|   _____   _|_|_   _|_|_   _|_|_   _\_/_   _|_|_  \__,_|   _|_|_  
_|"""""|_|"""""|_|"""""|_|     |_|"""""|_|"""""|_|"""""|_|"""""|_|"""""|_|"""""|_|"""""| 
"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-' 

(Font: ASCII - Train)

"El Psy Kongroo." -- Hououin Kyoma

"私は極色カスタ推しです...だが、狽音ウルシと夜鳴トバリも推す :)" -- Yukii_P

*/

H Head out to the Target

对每个时间段，找目标点的第一个被标记的祖先，如果二者距离小于等于r-l+1则目标点可到达。否则从目标点的第r-l+1个祖先出发一直打标记，直到到达被标记的祖先。

倍增来做找祖先的操作，dfs预处理复杂度nlogn，每次询问logn，总复杂度O(nlogn+qlogn)。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
/*

This code template was updated by Yukii_P on 2025/4/4.

*/
#include <bits/stdc++.h>
#define FIO cin.tie(0); ios::sync_with_stdio(false)
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define TEST
#define TESTS int t = 1; cin >> t; while (t--)

#if 1
#define int i64
#define inf 0x3f3f3f3f3f3f3f3fLL
#else
#define inf 0x3f3f3f3f
#endif

#ifndef ONLINE_JUDGE
#define debug(...) std::cerr << #__VA_ARGS__ << " = "; dbg1(__VA_ARGS__)
void dbg2() { std::cerr << "\n"; }
template<typename T, typename... T2>
void dbg2(T x, T2... args) {
    std::cerr << ", " << x;
    dbg2(args...);
}
template<typename T, typename... T2>
void dbg1(T x, T2... args) {
    std::cerr << x;
    dbg2(args...);
}
#else
#define debug(...) 
#endif

using namespace std;
using i64 = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using pii = std::pair<int, int>;

inline char nc() {
    static char buf[1 << 20], *p1, *p2;
    return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 20, stdin), p1 == p2) ? EOF : *p1++;
}
#ifndef ONLINE_JUDGE
#define nc getchar
#endif
void read() {}
template<typename T, typename... T2> 
inline void read(T &x, T2 &... oth) {
    x = 0; char c = nc(), up = c;
    while(!isdigit(c)) up = c, c = nc();
    while(isdigit(c)) x = x * 10 + c - '0', c = nc();
    up == '-' ? x = -x : 0;
    read(oth...);
}

constexpr int N = 2e5 + 10;
constexpr int MOD = 998244353;

void solve() {
    int n, k;
    cin >> n >> k;
    vector<int> f(n + 1), d(n + 1);
    vector<int> vis(n + 1);
    vector<array<int, 25>> fa(n + 1);
    vector<vector<int>> e(n + 1);
    for (int i = 2; i <= n; ++i) {
        cin >> fa[i][0];
        // e[i].push_back(fa[i][0]);
        e[fa[i][0]].push_back(i);
    }
    auto dfs = [&](auto&& dfs, int u) -> void {
        d[u] = d[fa[u][0]] + 1;
        for (int i = 1; i <= 24; ++i) {
            fa[u][i] = fa[fa[u][i - 1]][i - 1];
        }
        for (int v : e[u]) {
            //if (v == f) continue;
            dfs(dfs, v);
        }
    };
    dfs(dfs, 1);
    // for (int i = 1; i <= n; ++i) cout << d[i] << " \n"[i == n];

    vis[1] = 1;
    while (k--) {
        int u, l, r;
        cin >> u >> l >> r;
        if (vis[u]) {
            cout << l << "\n";
            return;
        }
        int t = r - l + 1;
        int v = u;
        // while (!vis[v]) {
        //     v = fa[v][0];
        // }

        for (int i = 24; i >= 0; --i) {
            if (fa[v][i] && !vis[fa[v][i]]) v = fa[v][i];
        }
        v = fa[v][0];
        debug(v);

        //debug(u, v, d[u], d[v]);
        if (d[u] - d[v] <= t) {
            cout << l + d[u] - d[v] - 1 << "\n";
            return;
        }
        int dd = d[u] - d[v];
        int x = u;

        // while (d[u] - d[x] < dd - t) x = fa[x][0];

        for (int i = 24; i >= 0; --i) {
            if (fa[x][i] && d[u] - d[fa[x][i]] < dd - t - 1) x = fa[x][i];
        }
        x = fa[x][0];
        debug(x);

        //debug(t, x, d[u] - d[x]);
        while (x != v) {
            vis[x] = 1;
            x = fa[x][0];
        }
    }
    cout << -1 << "\n";
}

signed main() {
    
    FIO;
    TEST {
        solve();
    }

    return 0;
}

/*

  _  _                            _____             _               _               _    
 | \| |    ___    _ _      ___   |_   _|    _ _    (_)    __ __    (_)    __ _     | |   
 | .` |   / _ \  | ' \    |___|    | |     | '_|   | |    \ V /    | |   / _` |    | |   
 |_|\_|   \___/  |_||_|   _____   _|_|_   _|_|_   _|_|_   _\_/_   _|_|_  \__,_|   _|_|_  
_|"""""|_|"""""|_|"""""|_|     |_|"""""|_|"""""|_|"""""|_|"""""|_|"""""|_|"""""|_|"""""| 
"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-' 

(Font: ASCII - Train)

"El Psy Kongroo." -- Hououin Kyoma

"私は極色カスタ推しです...だが、狽音ウルシと夜鳴トバリも推す :)" -- Yukii_P

*/

I Infinity

究竟是谁在做这种题。什么置换什么轮换完全不明白。反正就是设出轮换结构，对每个固定的轮换结构有个式子，是一个连乘的多项式，先ln转连加，整体加完再exp得到原式。所以式子怎么出来的。不懂。（）

抄了个猴妈妈的板子。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
/*

This code template was updated by Yukii_P on 2025/4/4.

*/
#include <bits/stdc++.h>
#define FIO cin.tie(0); ios::sync_with_stdio(false)
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define TEST
#define TESTS int t = 1; cin >> t; while (t--)

#if 0
#define int i64
#define inf 0x3f3f3f3f3f3f3f3fLL
#else
#define inf 0x3f3f3f3f
#endif

#ifndef ONLINE_JUDGE
#define debug(...) std::cerr << #__VA_ARGS__ << " = "; dbg1(__VA_ARGS__)
void dbg2() { std::cerr << "\n"; }
template<typename T, typename... T2>
void dbg2(T x, T2... args) {
    std::cerr << ", " << x;
    dbg2(args...);
}
template<typename T, typename... T2>
void dbg1(T x, T2... args) {
    std::cerr << x;
    dbg2(args...);
}
#else
#define debug(...) 
#endif

using namespace std;
using i64 = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using pii = std::pair<int, int>;

inline char nc() {
    static char buf[1 << 20], *p1, *p2;
    return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 20, stdin), p1 == p2) ? EOF : *p1++;
}
#ifndef ONLINE_JUDGE
#define nc getchar
#endif
void read() {}
template<typename T, typename... T2> 
inline void read(T &x, T2 &... oth) {
    x = 0; char c = nc(), up = c;
    while(!isdigit(c)) up = c, c = nc();
    while(isdigit(c)) x = x * 10 + c - '0', c = nc();
    up == '-' ? x = -x : 0;
    read(oth...);
}

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353U;
constexpr unsigned MO2 = 2U * MO;
constexpr int FFT_MAX = 23;
using Mint = ModInt<MO>;
constexpr Mint FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U, 166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U, 733596141U, 267099868U, 15311432U};
constexpr Mint INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U, 685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U, 428961804U, 382752275U, 469870224U};
constexpr Mint FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U, 856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U, 867605899U};
constexpr Mint INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U, 90816748U, 860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U, 824071951U, 103369235U};

// as[rev(i)] <- \sum_j \zeta^(ij) as[j]
void fft(Mint *as, int n) {
  assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
  int m = n;
  if (m >>= 1) {
    for (int i = 0; i < m; ++i) {
      const unsigned x = as[i + m].x;  // < MO
      as[i + m].x = as[i].x + MO - x;  // < 2 MO
      as[i].x += x;  // < 2 MO
    }
  }
  if (m >>= 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + m; ++i) {
        const unsigned x = (prod * as[i + m]).x;  // < MO
        as[i + m].x = as[i].x + MO - x;  // < 3 MO
        as[i].x += x;  // < 3 MO
      }
      prod *= FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  for (; m; ) {
    if (m >>= 1) {
      Mint prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < MO
          as[i + m].x = as[i].x + MO - x;  // < 4 MO
          as[i].x += x;  // < 4 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
    if (m >>= 1) {
      Mint prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < MO
          as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
          as[i + m].x = as[i].x + MO - x;  // < 3 MO
          as[i].x += x;  // < 3 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
    as[i].x = (as[i].x >= MO) ? (as[i].x - MO) : as[i].x;  // < MO
  }
}

// as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]
void invFft(Mint *as, int n) {
  assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
  int m = 1;
  if (m < n >> 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + m; ++i) {
        const unsigned long long y = as[i].x + MO - as[i + m].x;  // < 2 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
    }
    m <<= 1;
  }
  for (; m < n >> 1; m <<= 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + (m >> 1); ++i) {
        const unsigned long long y = as[i].x + MO2 - as[i + m].x;  // < 4 MO
        as[i].x += as[i + m].x;  // < 4 MO
        as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      for (int i = i0 + (m >> 1); i < i0 + m; ++i) {
        const unsigned long long y = as[i].x + MO - as[i + m].x;  // < 2 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  if (m < n) {
    for (int i = 0; i < m; ++i) {
      const unsigned y = as[i].x + MO2 - as[i + m].x;  // < 4 MO
      as[i].x += as[i + m].x;  // < 4 MO
      as[i + m].x = y;  // < 4 MO
    }
  }
  const Mint invN = Mint(n).inv();
  for (int i = 0; i < n; ++i) {
    as[i] *= invN;
  }
}

void fft(vector<Mint> &as) {
  fft(as.data(), as.size());
}
void invFft(vector<Mint> &as) {
  invFft(as.data(), as.size());
}

vector<Mint> convolve(vector<Mint> as, vector<Mint> bs) {
  if (as.empty() || bs.empty()) return {};
  const int len = as.size() + bs.size() - 1;
  int n = 1;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  bs.resize(n); fft(bs);
  for (int i = 0; i < n; ++i) as[i] *= bs[i];
  invFft(as);
  as.resize(len);
  return as;
}
vector<Mint> square(vector<Mint> as) {
  if (as.empty()) return {};
  const int len = as.size() + as.size() - 1;
  int n = 1;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  for (int i = 0; i < n; ++i) as[i] *= as[i];
  invFft(as);
  as.resize(len);
  return as;
}
// m := |as|, n := |bs|
// cs[k] = \sum[i-j=k] as[i] bs[j]  (0 <= k <= m-n)
// transpose of ((multiply by bs): K^[0,m-n] -> K^[0,m-1])
vector<Mint> middle(vector<Mint> as, vector<Mint> bs) {
  const int m = as.size(), n = bs.size();
  assert(m >= n); assert(n >= 1);
  int len = 1;
  for (; len < m; len <<= 1) {}
  as.resize(len, 0);
  fft(as);
  std::reverse(bs.begin(), bs.end());
  bs.resize(len, 0);
  fft(bs);
  for (int i = 0; i < len; ++i) as[i] *= bs[i];
  invFft(as);
  as.resize(m);
  as.erase(as.begin(), as.begin() + (n - 1));
  return as;
}
////////////////////////////////////////////////////////////////////////////////

////////////////////////////////////////////////////////////////////////////////
// inv: log, exp, pow
// fac: shift
// invFac: shift
constexpr int LIM_INV = 1 << 20;  // @
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];
struct ModIntPreparator {
  ModIntPreparator() {
    inv[1] = 1;
    for (int i = 2; i < LIM_INV; ++i) inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
    fac[0] = 1;
    for (int i = 1; i < LIM_INV; ++i) fac[i] = fac[i - 1] * i;
    invFac[0] = 1;
    for (int i = 1; i < LIM_INV; ++i) invFac[i] = invFac[i - 1] * inv[i];
  }
} preparator;

// polyWork0: *, inv, div, divAt, log, exp, pow, sqrt, shift
// polyWork1: inv, div, divAt, log, exp, pow, sqrt, shift
// polyWork2: divAt, exp, pow, sqrt
// polyWork3: exp, pow, sqrt
static constexpr int LIM_POLY = 1 << 20;  // @
static_assert(LIM_POLY <= 1 << FFT_MAX, "Poly: LIM_POLY <= 1 << FFT_MAX must hold.");
static Mint polyWork0[LIM_POLY], polyWork1[LIM_POLY], polyWork2[LIM_POLY], polyWork3[LIM_POLY];

struct Poly : public vector<Mint> {
  Poly() {}
  explicit Poly(int n) : vector<Mint>(n) {}
  Poly(const vector<Mint> &vec) : vector<Mint>(vec) {}
  Poly(std::initializer_list<Mint> il) : vector<Mint>(il) {}
  int size() const { return vector<Mint>::size(); }
  Mint at(long long k) const { return (0 <= k && k < size()) ? (*this)[k] : 0U; }
  int ord() const { for (int i = 0; i < size(); ++i) if ((*this)[i]) return i; return -1; }
  int deg() const { for (int i = size(); --i >= 0; ) if ((*this)[i]) return i; return -1; }
  Poly mod(int n) const { return Poly(vector<Mint>(data(), data() + min(max(n, 0), size()))); }
  Poly operator>>(int n) const { return Poly(vector<Mint>(data() + min(max(n, 0), size()), data() + size())); }
  Poly operator<<(int n) const { Poly fs = *this; fs.insert(fs.begin(), max(n, 0), 0); return fs; }
  friend std::ostream &operator<<(std::ostream &os, const Poly &fs) {
    os << "[";
    for (int i = 0; i < fs.size(); ++i) { if (i > 0) os << ", "; os << fs[i]; }
    return os << "]";
  }

  Poly &operator+=(const Poly &fs) {
    if (size() < fs.size()) resize(fs.size());
    for (int i = 0; i < fs.size(); ++i) (*this)[i] += fs[i];
    return *this;
  }
  Poly &operator-=(const Poly &fs) {
    if (size() < fs.size()) resize(fs.size());
    for (int i = 0; i < fs.size(); ++i) (*this)[i] -= fs[i];
    return *this;
  }
  // 3 E(|t| + |f|)
  Poly &operator*=(const Poly &fs) {
    if (empty() || fs.empty()) return *this = {};
    const int nt = size(), nf = fs.size();
    int n = 1;
    for (; n < nt + nf - 1; n <<= 1) {}
    assert(n <= LIM_POLY);
    resize(n);
    fft(data(), n);  // 1 E(n)
    memcpy(polyWork0, fs.data(), nf * sizeof(Mint));
    memset(polyWork0 + nf, 0, (n - nf) * sizeof(Mint));
    fft(polyWork0, n);  // 1 E(n)
    for (int i = 0; i < n; ++i) (*this)[i] *= polyWork0[i];
    invFft(data(), n);  // 1 E(n)
    resize(nt + nf - 1);
    return *this;
  }
  // 13 E(deg(t) - deg(f) + 1)
  // rev(t) = rev(f) rev(q) + x^(deg(t)-deg(f)+1) rev(r)
  Poly &operator/=(const Poly &fs) {
    const int m = deg(), n = fs.deg();
    assert(n != -1);
    if (m < n) return *this = {};
    Poly tsRev(m - n + 1), fsRev(min(m - n, n) + 1);
    for (int i = 0; i <= m - n; ++i) tsRev[i] = (*this)[m - i];
    for (int i = 0, i0 = min(m - n, n); i <= i0; ++i) fsRev[i] = fs[n - i];
    const Poly qsRev = tsRev.div(fsRev, m - n + 1);  // 13 E(m - n + 1)
    resize(m - n + 1);
    for (int i = 0; i <= m - n; ++i) (*this)[i] = qsRev[m - n - i];
    return *this;
  }
  // 13 E(deg(t) - deg(f) + 1) + 3 E(|t|)
  Poly &operator%=(const Poly &fs) {
    const Poly qs = *this / fs;  // 13 E(deg(t) - deg(f) + 1)
    *this -= fs * qs;  // 3 E(|t|)
    resize(deg() + 1);
    return *this;
  }
  Poly &operator*=(const Mint &a) {
    for (int i = 0; i < size(); ++i) (*this)[i] *= a;
    return *this;
  }
  Poly &operator/=(const Mint &a) {
    const Mint b = a.inv();
    for (int i = 0; i < size(); ++i) (*this)[i] *= b;
    return *this;
  }
  Poly operator+() const { return *this; }
  Poly operator-() const {
    Poly fs(size());
    for (int i = 0; i < size(); ++i) fs[i] = -(*this)[i];
    return fs;
  }
  Poly operator+(const Poly &fs) const { return (Poly(*this) += fs); }
  Poly operator-(const Poly &fs) const { return (Poly(*this) -= fs); }
  Poly operator*(const Poly &fs) const { return (Poly(*this) *= fs); }
  Poly operator/(const Poly &fs) const { return (Poly(*this) /= fs); }
  Poly operator%(const Poly &fs) const { return (Poly(*this) %= fs); }
  Poly operator*(const Mint &a) const { return (Poly(*this) *= a); }
  Poly operator/(const Mint &a) const { return (Poly(*this) /= a); }
  friend Poly operator*(const Mint &a, const Poly &fs) { return fs * a; }

  // 10 E(n)
  // f <- f - (t f - 1) f
  Poly inv(int n) const {
    assert(!empty()); assert((*this)[0]); assert(1 <= n);
    assert(n == 1 || 1 << (32 - __builtin_clz(n - 1)) <= LIM_POLY);
    Poly fs(n);
    fs[0] = (*this)[0].inv();
    for (int m = 1; m < n; m <<= 1) {
      memcpy(polyWork0, data(), min(m << 1, size()) * sizeof(Mint));
      memset(polyWork0 + min(m << 1, size()), 0, ((m << 1) - min(m << 1, size())) * sizeof(Mint));
      fft(polyWork0, m << 1);  // 2 E(n)
      memcpy(polyWork1, fs.data(), min(m << 1, n) * sizeof(Mint));
      memset(polyWork1 + min(m << 1, n), 0, ((m << 1) - min(m << 1, n)) * sizeof(Mint));
      fft(polyWork1, m << 1);  // 2 E(n)
      for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];
      invFft(polyWork0, m << 1); // 2 E(n)
      memset(polyWork0, 0, m * sizeof(Mint));
      fft(polyWork0, m << 1); // 2 E(n)
      for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];
      invFft(polyWork0, m << 1); // 2 E(n)
      for (int i = m, i0 = min(m << 1, n); i < i0; ++i) fs[i] = -polyWork0[i];
    }
    return fs;
  }
  // 9 E(n)
  // Need (4 m)-th roots of unity to lift from (mod x^m) to (mod x^(2m)).
  // f <- f - (t f - 1) f
  // (t f^2) mod ((x^(2m) - 1) (x^m - 1^(1/4)))
  /*
  Poly inv(int n) const {
    assert(!empty()); assert((*this)[0]); assert(1 <= n);
    assert(n == 1 || 3 << (31 - __builtin_clz(n - 1)) <= LIM_POLY);
    assert(n <= 1 << (FFT_MAX - 1));
    Poly fs(n);
    fs[0] = (*this)[0].inv();
    for (int h = 2, m = 1; m < n; ++h, m <<= 1) {
      const Mint a = FFT_ROOTS[h], b = INV_FFT_ROOTS[h];
      memcpy(polyWork0, data(), min(m << 1, size()) * sizeof(Mint));
      memset(polyWork0 + min(m << 1, size()), 0, ((m << 1) - min(m << 1, size())) * sizeof(Mint));
      {
        Mint aa = 1;
        for (int i = 0; i < m; ++i) { polyWork0[(m << 1) + i] = aa * polyWork0[i]; aa *= a; }
        for (int i = 0; i < m; ++i) { polyWork0[(m << 1) + i] += aa * polyWork0[m + i]; aa *= a; }
      }
      fft(polyWork0, m << 1);  // 2 E(n)
      fft(polyWork0 + (m << 1), m);  // 1 E(n)
      memcpy(polyWork1, fs.data(), min(m << 1, n) * sizeof(Mint));
      memset(polyWork1 + min(m << 1, n), 0, ((m << 1) - min(m << 1, n)) * sizeof(Mint));
      {
        Mint aa = 1;
        for (int i = 0; i < m; ++i) { polyWork1[(m << 1) + i] = aa * polyWork1[i]; aa *= a; }
        for (int i = 0; i < m; ++i) { polyWork1[(m << 1) + i] += aa * polyWork1[m + i]; aa *= a; }
      }
      fft(polyWork1, m << 1);  // 2 E(n)
      fft(polyWork1 + (m << 1), m);  // 1 E(n)
      for (int i = 0; i < (m << 1) + m; ++i) polyWork0[i] *= polyWork1[i] * polyWork1[i];
      invFft(polyWork0, m << 1);  // 2 E(n)
      invFft(polyWork0 + (m << 1), m);  // 1 E(n)
      // 2 f0 + (-f2), (-f1) + (-f3), 1^(1/4) (-f1) - (-f2) - 1^(1/4) (-f3)
      {
        Mint bb = 1;
        for (int i = 0, i0 = min(m, n - m); i < i0; ++i) {
          unsigned x = polyWork0[i].x + (bb * polyWork0[(m << 1) + i]).x + MO2 - (fs[i].x << 1);  // < 4 MO
          fs[m + i] = Mint(static_cast<unsigned long long>(FFT_ROOTS[2].x) * x) - polyWork0[m + i];
          fs[m + i].x = ((fs[m + i].x & 1) ? (fs[m + i].x + MO) : fs[m + i].x) >> 1;
          bb *= b;
        }
      }
    }
    return fs;
  }
  */
  // 13 E(n)
  // g = (1 / f) mod x^m
  // h <- h - (f h - t) g
  Poly div(const Poly &fs, int n) const {
    assert(!fs.empty()); assert(fs[0]); assert(1 <= n);
    if (n == 1) return {at(0) / fs[0]};
    // m < n <= 2 m
    const int m = 1 << (31 - __builtin_clz(n - 1));
    assert(m << 1 <= LIM_POLY);
    Poly gs = fs.inv(m);  // 5 E(n)
    gs.resize(m << 1);
    fft(gs.data(), m << 1);  // 1 E(n)
    if (size()) memcpy(polyWork0, data(), min(m, size()) * sizeof(Mint));
    memset(polyWork0 + min(m, size()), 0, ((m << 1) - min(m, size())) * sizeof(Mint));
    fft(polyWork0, m << 1);  // 1 E(n)
    for (int i = 0; i < m << 1; ++i) polyWork0[i] *= gs[i];
    invFft(polyWork0, m << 1);  // 1 E(n)
    Poly hs(n);
    memcpy(hs.data(), polyWork0, m * sizeof(Mint));
    memset(polyWork0 + m, 0, m * sizeof(Mint));
    fft(polyWork0, m << 1);  // 1 E(n)
    memcpy(polyWork1, fs.data(), min(m << 1, fs.size()) * sizeof(Mint));
    memset(polyWork1 + min(m << 1, fs.size()), 0, ((m << 1) - min(m << 1, fs.size())) * sizeof(Mint));
    fft(polyWork1, m << 1);  // 1 E(n)
    for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];
    invFft(polyWork0, m << 1);  // 1 E(n)
    memset(polyWork0, 0, m * sizeof(Mint));
    for (int i = m, i0 = min(m << 1, size()); i < i0; ++i) polyWork0[i] -= (*this)[i];
    fft(polyWork0, m << 1);  // 1 E(n)
    for (int i = 0; i < m << 1; ++i) polyWork0[i] *= gs[i];
    invFft(polyWork0, m << 1);  // 1 E(n)
    for (int i = m; i < n; ++i) hs[i] = -polyWork0[i];
    return hs;
  }
  // (4 (floor(log_2 k) - ceil(log_2 |f|)) + 16) E(|f|)  for  |t| < |f|
  // [x^k] (t(x) / f(x)) = [x^k] ((t(x) f(-x)) / (f(x) f(-x))
  // polyWork0: half of (2 m)-th roots of unity, inversed, bit-reversed
  Mint divAt(const Poly &fs, long long k) const {
    assert(k >= 0);
    if (size() >= fs.size()) {
      const Poly qs = *this / fs;  // 13 E(deg(t) - deg(f) + 1)
      Poly rs = *this - fs * qs;  // 3 E(|t|)
      rs.resize(rs.deg() + 1);
      return qs.at(k) + rs.divAt(fs, k);
    }
    int h = 0, m = 1;
    for (; m < fs.size(); ++h, m <<= 1) {}
    if (k < m) {
      const Poly gs = fs.inv(k + 1);  // 10 E(|f|)
      Mint sum;
      for (int i = 0, i0 = min<int>(k + 1, size()); i < i0; ++i) sum += (*this)[i] * gs[k - i];
      return sum;
    }
    assert(m << 1 <= LIM_POLY);
    polyWork0[0] = Mint(2U).inv();
    for (int hh = 0; hh < h; ++hh) for (int i = 0; i < 1 << hh; ++i) polyWork0[1 << hh | i] = polyWork0[i] * INV_FFT_ROOTS[hh + 2];
    const Mint a = FFT_ROOTS[h + 1];
    if (size()) memcpy(polyWork2, data(), size() * sizeof(Mint));
    memset(polyWork2 + size(), 0, ((m << 1) - size()) * sizeof(Mint));
    fft(polyWork2, m << 1);  // 2 E(|f|)
    memcpy(polyWork1, fs.data(), fs.size() * sizeof(Mint));
    memset(polyWork1 + fs.size(), 0, ((m << 1) - fs.size()) * sizeof(Mint));
    fft(polyWork1, m << 1);  // 2 E(|f|)
    for (; ; ) {
      if (k & 1) {
        for (int i = 0; i < m; ++i) polyWork2[i] = polyWork0[i] * (polyWork2[i << 1 | 0] * polyWork1[i << 1 | 1] - polyWork2[i << 1 | 1] * polyWork1[i << 1 | 0]);
      } else {
        for (int i = 0; i < m; ++i) {
          polyWork2[i] = polyWork2[i << 1 | 0] * polyWork1[i << 1 | 1] + polyWork2[i << 1 | 1] * polyWork1[i << 1 | 0];
          polyWork2[i].x = ((polyWork2[i].x & 1) ? (polyWork2[i].x + MO) : polyWork2[i].x) >> 1;
        }
      }
      for (int i = 0; i < m; ++i) polyWork1[i] = polyWork1[i << 1 | 0] * polyWork1[i << 1 | 1];
      if ((k >>= 1) < m) {
        invFft(polyWork2, m);  // 1 E(|f|)
        invFft(polyWork1, m);  // 1 E(|f|)
        // Poly::inv does not use polyWork2
        const Poly gs = Poly(vector<Mint>(polyWork1, polyWork1 + k + 1)).inv(k + 1);  // 10 E(|f|)
        Mint sum;
        for (int i = 0; i <= k; ++i) sum += polyWork2[i] * gs[k - i];
        return sum;
      }
      memcpy(polyWork2 + m, polyWork2, m * sizeof(Mint));
      invFft(polyWork2 + m, m);  // (floor(log_2 k) - ceil(log_2 |f|)) E(|f|)
      memcpy(polyWork1 + m, polyWork1, m * sizeof(Mint));
      invFft(polyWork1 + m, m);  // (floor(log_2 k) - ceil(log_2 |f|)) E(|f|)
      Mint aa = 1;
      for (int i = m; i < m << 1; ++i) { polyWork2[i] *= aa; polyWork1[i] *= aa; aa *= a; }
      fft(polyWork2 + m, m);  // (floor(log_2 k) - ceil(log_2 |f|)) E(|f|)
      fft(polyWork1 + m, m);  // (floor(log_2 k) - ceil(log_2 |f|)) E(|f|)
    }
  }
  // 13 E(n)
  // D log(t) = (D t) / t
  Poly log(int n) const {
    assert(!empty()); assert((*this)[0].x == 1U); assert(n <= LIM_INV);
    Poly fs = mod(n);
    for (int i = 0; i < fs.size(); ++i) fs[i] *= i;
    fs = fs.div(*this, n);
    for (int i = 1; i < n; ++i) fs[i] *= ::inv[i];
    return fs;
  }
  // (16 + 1/2) E(n)
  // f = exp(t) mod x^m  ==>  (D f) / f == D t  (mod x^m)
  // g = (1 / exp(t)) mod x^m
  // f <- f - (log f - t) / (1 / f)
  //   =  f - (I ((D f) / f) - t) f
  //   == f - (I ((D f) / f + (f g - 1) ((D f) / f - D (t mod x^m))) - t) f  (mod x^(2m))
  //   =  f - (I (g (D f - f D (t mod x^m)) + D (t mod x^m)) - t) f
  // g <- g - (f g - 1) g
  // polyWork1: DFT(f, 2 m), polyWork2: g, polyWork3: DFT(g, 2 m)
  Poly exp(int n) const {
    assert(!empty()); assert(!(*this)[0]); assert(1 <= n);
    assert(n == 1 || 1 << (32 - __builtin_clz(n - 1)) <= min(LIM_INV, LIM_POLY));
    if (n == 1) return {1U};
    if (n == 2) return {1U, at(1)};
    Poly fs(n);
    fs[0].x = polyWork1[0].x = polyWork1[1].x = polyWork2[0].x = 1U;
    int m;
    for (m = 1; m << 1 < n; m <<= 1) {
      for (int i = 0, i0 = min(m, size()); i < i0; ++i) polyWork0[i] = i * (*this)[i];
      memset(polyWork0 + min(m, size()), 0, (m - min(m, size())) * sizeof(Mint));
      fft(polyWork0, m);  // (1/2) E(n)
      for (int i = 0; i < m; ++i) polyWork0[i] *= polyWork1[i];
      invFft(polyWork0, m);  // (1/2) E(n)
      for (int i = 0; i < m; ++i) polyWork0[i] -= i * fs[i];
      memset(polyWork0 + m, 0, m * sizeof(Mint));
      fft(polyWork0, m << 1);  // 1 E(n)
      memcpy(polyWork3, polyWork2, m * sizeof(Mint));
      memset(polyWork3 + m, 0, m * sizeof(Mint));
      fft(polyWork3, m << 1);  // 1 E(n)
      for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork3[i];
      invFft(polyWork0, m << 1);  // 1 E(n)
      for (int i = 0; i < m; ++i) polyWork0[i] *= ::inv[m + i];
      for (int i = 0, i0 = min(m, size() - m); i < i0; ++i) polyWork0[i] += (*this)[m + i];
      memset(polyWork0 + m, 0, m * sizeof(Mint));
      fft(polyWork0, m << 1);  // 1 E(n)
      for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];
      invFft(polyWork0, m << 1);  // 1 E(n)
      memcpy(fs.data() + m, polyWork0, m * sizeof(Mint));
      memcpy(polyWork1, fs.data(), (m << 1) * sizeof(Mint));
      memset(polyWork1 + (m << 1), 0, (m << 1) * sizeof(Mint));
      fft(polyWork1, m << 2);  // 2 E(n)
      for (int i = 0; i < m << 1; ++i) polyWork0[i] = polyWork1[i] * polyWork3[i];
      invFft(polyWork0, m << 1);  // 1 E(n)
      memset(polyWork0, 0, m * sizeof(Mint));
      fft(polyWork0, m << 1);  // 1 E(n)
      for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork3[i];
      invFft(polyWork0, m << 1);  // 1 E(n)
      for (int i = m; i < m << 1; ++i) polyWork2[i] = -polyWork0[i];
    }
    for (int i = 0, i0 = min(m, size()); i < i0; ++i) polyWork0[i] = i * (*this)[i];
    memset(polyWork0 + min(m, size()), 0, (m - min(m, size())) * sizeof(Mint));
    fft(polyWork0, m);  // (1/2) E(n)
    for (int i = 0; i < m; ++i) polyWork0[i] *= polyWork1[i];
    invFft(polyWork0, m);  // (1/2) E(n)
    for (int i = 0; i < m; ++i) polyWork0[i] -= i * fs[i];
    memcpy(polyWork0 + m, polyWork0 + (m >> 1), (m >> 1) * sizeof(Mint));
    memset(polyWork0 + (m >> 1), 0, (m >> 1) * sizeof(Mint));
    memset(polyWork0 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));
    fft(polyWork0, m);  // (1/2) E(n)
    fft(polyWork0 + m, m);  // (1/2) E(n)
    memcpy(polyWork3 + m, polyWork2 + (m >> 1), (m >> 1) * sizeof(Mint));
    memset(polyWork3 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));
    fft(polyWork3 + m, m);  // (1/2) E(n)
    for (int i = 0; i < m; ++i) polyWork0[m + i] = polyWork0[i] * polyWork3[m + i] + polyWork0[m + i] * polyWork3[i];
    for (int i = 0; i < m; ++i) polyWork0[i] *= polyWork3[i];
    invFft(polyWork0, m);  // (1/2) E(n)
    invFft(polyWork0 + m, m);  // (1/2) E(n)
    for (int i = 0; i < m >> 1; ++i) polyWork0[(m >> 1) + i] += polyWork0[m + i];
    for (int i = 0; i < m; ++i) polyWork0[i] *= ::inv[m + i];
    for (int i = 0, i0 = min(m, size() - m); i < i0; ++i) polyWork0[i] += (*this)[m + i];
    memset(polyWork0 + m, 0, m * sizeof(Mint));
    fft(polyWork0, m << 1);  // 1 E(n)
    for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];
    invFft(polyWork0, m << 1);  // 1 E(n)
    memcpy(fs.data() + m, polyWork0, (n - m) * sizeof(Mint));
    return fs;
  }
  // (29 + 1/2) E(n)
  // g <- g - (log g - a log t) g
  Poly pow1(Mint a, int n) const {
    assert(!empty()); assert((*this)[0].x == 1U); assert(1 <= n);
    return (a * log(n)).exp(n);  // 13 E(n) + (16 + 1/2) E(n)
  }
  // (29 + 1/2) E(n - a ord(t))
  Poly pow(long long a, int n) const {
    assert(a >= 0); assert(1 <= n);
    if (a == 0) { Poly gs(n); gs[0].x = 1U; return gs; }
    const int o = ord();
    if (o == -1 || o > (n - 1) / a) return Poly(n);
    const Mint b = (*this)[o].inv(), c = (*this)[o].pow(a);
    const int ntt = min<int>(n - a * o, size() - o);
    Poly tts(ntt);
    for (int i = 0; i < ntt; ++i) tts[i] = b * (*this)[o + i];
    tts = tts.pow1(a, n - a * o);  // (29 + 1/2) E(n - a ord(t))
    Poly gs(n);
    for (int i = 0; i < n - a * o; ++i) gs[a * o + i] = c * tts[i];
    return gs;
  }
  // (10 + 1/2) E(n)
  // f = t^(1/2) mod x^m,  g = 1 / t^(1/2) mod x^m
  // f <- f - (f^2 - h) g / 2
  // g <- g - (f g - 1) g
  // polyWork1: DFT(f, m), polyWork2: g, polyWork3: DFT(g, 2 m)
  Poly sqrt(int n) const {
    assert(!empty()); assert((*this)[0].x == 1U); assert(1 <= n);
    assert(n == 1 || 1 << (32 - __builtin_clz(n - 1)) <= LIM_POLY);
    if (n == 1) return {1U};
    if (n == 2) return {1U, at(1) / 2};
    Poly fs(n);
    fs[0].x = polyWork1[0].x = polyWork2[0].x = 1U;
    int m;
    for (m = 1; m << 1 < n; m <<= 1) {
      for (int i = 0; i < m; ++i) polyWork1[i] *= polyWork1[i];
      invFft(polyWork1, m);  // (1/2) E(n)
      for (int i = 0, i0 = min(m, size()); i < i0; ++i) polyWork1[i] -= (*this)[i];
      for (int i = 0, i0 = min(m, size() - m); i < i0; ++i) polyWork1[i] -= (*this)[m + i];
      memset(polyWork1 + m, 0, m * sizeof(Mint));
      fft(polyWork1, m << 1);  // 1 E(n)
      memcpy(polyWork3, polyWork2, m * sizeof(Mint));
      memset(polyWork3 + m, 0, m * sizeof(Mint));
      fft(polyWork3, m << 1);  // 1 E(n)
      for (int i = 0; i < m << 1; ++i) polyWork1[i] *= polyWork3[i];
      invFft(polyWork1, m << 1);  // 1 E(n)
      for (int i = 0; i < m; ++i) { polyWork1[i] = -polyWork1[i]; fs[m + i].x = ((polyWork1[i].x & 1) ? (polyWork1[i].x + MO) : polyWork1[i].x) >> 1; }
      memcpy(polyWork1, fs.data(), (m << 1) * sizeof(Mint));
      fft(polyWork1, m << 1);  // 1 E(n)
      for (int i = 0; i < m << 1; ++i) polyWork0[i] = polyWork1[i] * polyWork3[i];
      invFft(polyWork0, m << 1);  // 1 E(n)
      memset(polyWork0, 0, m * sizeof(Mint));
      fft(polyWork0, m << 1);  // 1 E(n)
      for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork3[i];
      invFft(polyWork0, m << 1);  // 1 E(n)
      for (int i = m; i < m << 1; ++i) polyWork2[i] = -polyWork0[i];
    }
    for (int i = 0; i < m; ++i) polyWork1[i] *= polyWork1[i];
    invFft(polyWork1, m);  // (1/2) E(n)
    for (int i = 0, i0 = min(m, size()); i < i0; ++i) polyWork1[i] -= (*this)[i];
    for (int i = 0, i0 = min(m, size() - m); i < i0; ++i) polyWork1[i] -= (*this)[m + i];
    memcpy(polyWork1 + m, polyWork1 + (m >> 1), (m >> 1) * sizeof(Mint));
    memset(polyWork1 + (m >> 1), 0, (m >> 1) * sizeof(Mint));
    memset(polyWork1 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));
    fft(polyWork1, m);  // (1/2) E(n)
    fft(polyWork1 + m, m);  // (1/2) E(n)
    memcpy(polyWork3 + m, polyWork2 + (m >> 1), (m >> 1) * sizeof(Mint));
    memset(polyWork3 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));
    fft(polyWork3 + m, m);  // (1/2) E(n)
    // for (int i = 0; i < m << 1; ++i) polyWork1[i] *= polyWork3[i];
    for (int i = 0; i < m; ++i) polyWork1[m + i] = polyWork1[i] * polyWork3[m + i] + polyWork1[m + i] * polyWork3[i];
    for (int i = 0; i < m; ++i) polyWork1[i] *= polyWork3[i];
    invFft(polyWork1, m);  // (1/2) E(n)
    invFft(polyWork1 + m, m);  // (1/2) E(n)
    for (int i = 0; i < m >> 1; ++i) polyWork1[(m >> 1) + i] += polyWork1[m + i];
    for (int i = 0; i < n - m; ++i) { polyWork1[i] = -polyWork1[i]; fs[m + i].x = ((polyWork1[i].x & 1) ? (polyWork1[i].x + MO) : polyWork1[i].x) >> 1; }
    return fs;
  }
  // (10 + 1/2) E(n)
  // modSqrt must return a quadratic residue if exists, or anything otherwise.
  // Return {} if *this does not have a square root.
  template <class F> Poly sqrt(int n, F modSqrt) const {
    assert(1 <= n);
    const int o = ord();
    if (o == -1) return Poly(n);
    if (o & 1) return {};
    const Mint c = modSqrt((*this)[o]);
    if (c * c != (*this)[o]) return {};
    if (o >> 1 >= n) return Poly(n);
    const Mint b = (*this)[o].inv();
    const int ntt = min(n - (o >> 1), size() - o);
    Poly tts(ntt);
    for (int i = 0; i < ntt; ++i) tts[i] = b * (*this)[o + i];
    tts = tts.sqrt(n - (o >> 1));  // (10 + 1/2) E(n)
    Poly gs(n);
    for (int i = 0; i < n - (o >> 1); ++i) gs[(o >> 1) + i] = c * tts[i];
    return gs;
  }
  // 6 E(|t|)
  // x -> x + a
  Poly shift(const Mint &a) const {
    if (empty()) return {};
    const int n = size();
    int m = 1;
    for (; m < n; m <<= 1) {}
    for (int i = 0; i < n; ++i) polyWork0[i] = fac[i] * (*this)[i];
    memset(polyWork0 + n, 0, ((m << 1) - n) * sizeof(Mint));
    fft(polyWork0, m << 1);  // 2 E(|t|)
    {
      Mint aa = 1;
      for (int i = 0; i < n; ++i) { polyWork1[n - 1 - i] = invFac[i] * aa; aa *= a; }
    }
    memset(polyWork1 + n, 0, ((m << 1) - n) * sizeof(Mint));
    fft(polyWork1, m << 1);  // 2 E(|t|)
    for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];
    invFft(polyWork0, m << 1);  // 2 E(|t|)
    Poly fs(n);
    for (int i = 0; i < n; ++i) fs[i] = invFac[i] * polyWork0[n - 1 + i];
    return fs;
  }
};

// 在线等一个又短，封装的又好的板子 我哭了。

void solve() {
    int t, k;
    cin >> t >> k;
    vector<int> query(t);
    for (auto& x : query) cin >> x;
    int M = ranges::max(query);
    Poly f(M + 1);
    for (int i = 1; i <= M; ++i) {
        int m = M / i;
        Poly g(m + 1);
        for (int j = 0; j <= m; ++j) {
            g[j] = (inv[i].pow(j) * invFac[j]).pow(k + 1);
        }
        g = g.log(m + 1);
        for (int j = 0; j <= m; ++j) f[i * j] += g[j];
    }
    f = f.exp(M + 1);
    for (auto x : query) {
        auto ans = f[x];
        ans *= fac[x].pow(k + 1);
        cout << ans.x << "\n";
    }
}

signed main() {
    
    FIO;
    solve();

    return 0;
}

/*

  _  _                            _____             _               _               _    
 | \| |    ___    _ _      ___   |_   _|    _ _    (_)    __ __    (_)    __ _     | |   
 | .` |   / _ \  | ' \    |___|    | |     | '_|   | |    \ V /    | |   / _` |    | |   
 |_|\_|   \___/  |_||_|   _____   _|_|_   _|_|_   _|_|_   _\_/_   _|_|_  \__,_|   _|_|_  
_|"""""|_|"""""|_|"""""|_|     |_|"""""|_|"""""|_|"""""|_|"""""|_|"""""|_|"""""|_|"""""| 
"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-'"`-0-0-' 

(Font: ASCII - Train)

"El Psy Kongroo." -- Hououin Kyoma

"私は極色カスタ推しです...だが、狽音ウルシと夜鳴トバリも推す :)" -- Yukii_P

*/

K Kaleidoscope

没补。有机会补。

G Gellyfish and Priority Queue

没补。有机会补。

唉概率论。