信息
- ID
- 124
- 时间
- 1000ms
- 内存
- 128MiB
- 难度
- 1
- 标签
- 递交数
- 37
- 已通过
- 34
- 上传者
/*****************************************
备注:
******************************************/
#include <queue>
#include <math.h>
#include <stack>
#include <stdio.h>
#include <iostream>
#include <vector>
#include <iomanip>
#include <string.h>
#include <algorithm>
using namespace std;
#define LL long long
const int N = 1e5 + 10;
const int mod = 999911659;
LL num[N],len , n1[5] , inv[5];
LL cc[5] = {0,2,3,4679,35617};
LL power(LL a, LL b ,LL m)
{
LL ans = 1;
while(b)
{
if(b&1)
ans = (ans * a) % m;
b >>= 1;
a = (a*a)%m;
}
return ans;
}
LL C(LL n , LL m , LL p)
{
if(n < m)
return 0;
if(m < n-m)
m = n-m;
LL ans ,sum;
ans = sum = 1;
for(int i = 0 ; i < m ; i++)
{
ans = (ans * (n-i))%p;
sum = (sum * (i+1))%p;
}
return (ans * power(sum , p-2 , p) ) %p;
}
LL lucas(LL n , LL m , LL p)
{
if(!m) return 1;
return (lucas(n/p , m/p , p) * C(n%p , m%p , p) )%p;
}
LL k[N];
LL CRT()
{
LL sums = 0;
for(int i = 1; i <= 4 ;i++)
sums = (sums + ((k[i]*n1[i])%(mod-1))*inv[i])%(mod-1);
return sums;
}
void init(LL n)
{
for(int i = 1 ; i *i < n ; i++)
if(n%i == 0)
num[len++] = i , num[len++] = n/i;
LL p = sqrt(n);
if(p*p == n)
num[len++] = p;
LL nums = mod - 1;
for(int i = 1 ;i <= 4; i++)
{
n1[i] = nums/cc[i];
inv[i] = power(n1[i] , cc[i]-2 , cc[i]);
}
}
int main()
{
LL n,q;
cin >> n >> q;
if(q%mod == 0)
{
cout << 0;
return 0;
}
init(n);
LL sum = 0;
for(int j = 1 ;j <= 4 ;j++)
for(int i = 0 ; i < len ; i++)
k[j] += lucas(n,num[i],cc[j]);
sum = CRT();
cout << power(q,sum,mod);
return 0;
}
C++ :
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<iostream>
#include<string>
#include<cstring>
#include<cmath>
//999911658=2*3*4679*35617
#define LL long long
#define mod 999911659
using namespace std;
LL N,G,e;
LL x[4];
LL pre[4][40000];
LL ni[4][40000];
LL zs[4]={2,3,4679,35617};
LL gcd(LL a,LL b,LL &x,LL &y)//求逆元
{
if(b==0) {x=1;y=0;}
else {gcd(b,a%b,y,x); y-=(a/b)*x;}
}
LL lucas(LL p,LL q,LL o)//卢卡斯定理
{
LL sum=1;
while(p && q)
{
LL x=p%zs[o],y=q%zs[o];
if(y>x) return 0;
sum=(sum*(pre[o][x]*(ni[o][x-y]*ni[o][y])%zs[o])%zs[o])%zs[o];
p/=zs[o];
q/=zs[o];
}
return sum;
}
int main()
{
scanf("%lld%lld",&N,&G);
if(G%mod==0) {printf("0\n");return 0;}
for(int o=0;o<4;o++)//预处理
{
pre[o][0]=1;ni[o][0]=1;
for(int i=1;i<=zs[o];i++)
pre[o][i]=(pre[o][i-1]*i)%zs[o];
ni[o][zs[o]-1]=zs[o]-1;
for(int i=zs[o]-2;i>=1;i--)
ni[o][i]=(ni[o][i+1]*(i+1))%zs[o];
for(LL i=1;i<=sqrt(N);i++)//统计组合数
if(N%i==0)
{
x[o]=(x[o]+lucas(N,i,o))%zs[o];
if(i*i<N) x[o]=(x[o]+lucas(N,N/i,o))%zs[o];
}
};
for(int i=0;i<4;i++)//中国剩余定理
{
LL o,p;
LL M=(mod-1)/zs[i];
gcd(M,zs[i],o,p);
e=(e+x[i]*o*M)%(mod-1);
}
while(e<=0) e+=mod-1;
LL ans=1,a=G;
while(e)
{
if(e&1) ans=(ans*a)%mod;
a=(a*a)%mod;
e>>=1;
}
printf("%lld\n",ans);
return 0;
}