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| #include<algorithm>
#include<iostream>
#include<iomanip>
#include<cstring>
#include<cstdlib>
#include<vector>
#include<cstdio>
#include<cmath>
#include<queue>
using namespace std;
typedef long long LL;
inline const LL Get_Int() {
LL num=0,bj=1;
char x=getchar();
while(x<'0'||x>'9') {
if(x=='-')bj=-1;
x=getchar();
}
while(x>='0'&&x<='9') {
num=num*10+x-'0';
x=getchar();
}
return num*bj;
}
const LL mod[]= {0,2,13,5281,7283},Mod=999999599;
LL n,g,f[10005][5],invf[10005][5];
LL C(LL n,LL m,int id) {
if(m>n)return 0;
return f[n][id]*invf[m][id]%mod[id]*invf[n-m][id]%mod[id];
}
LL Lucas(LL n,LL m,int id) {
if(!m)return 1;
return (C(n%mod[id],m%mod[id],id)*Lucas(n/mod[id],m/mod[id],id))%mod[id];
}
LL Quick_Pow(LL a,LL b,LL mod=Mod) {
LL ans=1;
while(b) {
if(b&1)ans=ans*a%mod;
a=a*a%mod;
b>>=1;
}
return ans;
}
LL inv(LL a,LL mod) {
return Quick_Pow(a,mod-2,mod);
}
LL Crt(const LL* a) {
LL ans=0;
for(int i=1; i<=4; i++) {
LL M=(Mod-1)/mod[i];
ans=(ans+M*inv(M,mod[i])*a[i])%(Mod-1);
}
return ans;
}
LL Solve(LL d) {
LL a[5];
for(int i=1; i<=4; i++)a[i]=Lucas(n,n/d,i);
LL ans=Crt(a);
return ans;
}
int main() {
for(int i=1; i<=4; i++) {
f[0][i]=invf[0][i]=1;
for(int j=1; j<=8000; j++) {
f[j][i]=f[j-1][i]*j%mod[i];
invf[j][i]=inv(f[j][i],mod[i]);
}
}
while(~scanf("%lld%lld",&n,&g)) {
if(g%Mod==0) {
puts("0");
continue;
}
LL sum=0;
for(LL d=1; d<=sqrt(n); d++)
if(n%d==0) {
sum=(sum+Solve(d))%(Mod-1);
if(d!=n/d)sum=(sum+Solve(n/d))%(Mod-1);
}
LL ans=Quick_Pow(g,sum);
printf("%lld\n",ans);
}
return 0;
}
|
