| 比赛 |
2026.5.30 |
评测结果 |
AAAAWWWWWW |
| 题目名称 |
数列求和 |
最终得分 |
40 |
| 用户昵称 |
郑霁桓 |
运行时间 |
1.347 s |
| 代码语言 |
C++ |
内存使用 |
3.69 MiB |
| 提交时间 |
2026-05-30 10:33:50 |
显示代码纯文本
#include<bits/stdc++.h>
using namespace std;
long long n,a,k,M,as,ps[2009],s,xx,yy;
inline long long pw(long long x,long long y){
long long ss=1;
while(y){
if(y&1) ss=ss*x%M;
x=x*x%M;
y>>=1;
}
return ss;
}
long long df(long long x,long long y){
if(y==0) return 1;
if(y==1) return x+1;
long long ss=df(x,(y-1)/2);
ss=(ss+ss*pw(x,(y-1)/2+1))%M;
if(y&1) return ss;
return (ss+pw(x,y))%M;
}
void exgcd(long long a,long long b,long long &x,long long &y){
if(!b){
x=1;
y=0;
return;
}
exgcd(b,a%b,x,y);
long long yy=y;
y=(x-(a/b)*y)%M;
x=yy;
return;
}
int main(){
freopen("oeis.in","r",stdin);
freopen("oeis.out","w",stdout);
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
cin>>n>>a>>k>>M;
a%=M;
if(n<=1000000){
for(long long i=1;i<=n;i++){
as=(as+pw(i,k)*pw(a,i))%M;
}
cout<<as;
return 0;
}
if(!k){
cout<<(df(a,n)-1+M)%M;
return 0;
}
if(a==1){
for(int i=1;i<=k+3;i++){
ps[i]=(ps[i-1]+pw(i,k))%M;
}
for(long long i=1;i<=k+3;i++){
long long s1=1,s2=1;
for(long long j=1;j<=k+3;j++){
if(i==j) continue;
s1=s1*(i-j)%M;
s2=s2*(n-j)%M;
}
s1=(s1%M+M)%M;
s2=(s2%M+M)%M;
exgcd(s1,M,xx,yy);
xx=(xx%M+M)%M;
s=(s+s2*xx%M*ps[i])%M;
}
s=(s%M+M)%M;
cout<<s;
return 0;
}
return 0;
}