| 比赛 |
2026.5.30 |
评测结果 |
AAAWAWWWWW |
| 题目名称 |
数列求和 |
最终得分 |
40 |
| 用户昵称 |
终焉折枝 |
运行时间 |
1.284 s |
| 代码语言 |
C++ |
内存使用 |
5.85 MiB |
| 提交时间 |
2026-05-30 12:02:28 |
显示代码纯文本
#include<iostream>
using namespace std;
typedef long long ll;
ll n, a, k, P;
ll S[2005][2005], C[2005];
ll qpow(ll x, ll y){
ll res = 1; x %= P;
for(;y;y >>= 1,x = x * x % P){
if(y & 1){
res = res * x % P;
}
}
return res;
}
ll inv(ll x){
return qpow(x, P - 2);
}
int main(){
freopen("oeis.in", "r", stdin);
freopen("oeis.out", "w", stdout);
cin >> n >> a >> k >> P;
if(n <= 1000000){
ll ans = 0;
for(int i = 1;i <= n;i ++) ans = (ans + qpow(i, k) * qpow(a, i)) % P;
cout << ans << "\n";
return 0;
}
if(k == 0){
if(a % P == 1) cout << n % P << "\n";
else cout << (a % P * (qpow(a, n) - 1 + P) % P * inv((a - 1 % P + P) % P)) % P << "\n";
return 0;
}
if(a % P == 1){
S[0][0] = 1;
for(int i = 1;i <= k;i ++)
for(int j = 1;j <= i;j ++)
S[i][j] = (S[i - 1][j - 1] + j * S[i - 1][j]) % P;
C[0] = 1;
for(int j = 1;j <= k + 1;j ++) C[j] = C[j - 1] * ((n + 1 - j + 1) % P) % P * inv(j) % P;
ll ans = 0, fac = 1;
for(int j = 0;j <= k;j ++){
ans = (ans + S[k][j] * fac % P * C[j + 1]) % P;
fac = fac * (j + 1) % P;
}
cout << ans << "\n";
return 0;
}
return 0;
}