Consider sequences \\{A_1,...,A_N\\} of length N consisting of integers between 1 and K (inclusive).

There are K^N such sequences. Find the sum of \gcd(A_1, ..., A_N) over all of them.

Since this sum can be enormous, print the value modulo (10^9+7).

Here \gcd(A_1, ..., A_N) denotes the greatest common divisor of A_1, ..., A_N.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq K \leq 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K


Output

Print the sum of \gcd(A_1, ..., A_N) over all K^N sequences, modulo (10^9+7).

Examples

Input

3 2


Output

9


Input

3 200


Output

10813692


Input

100000 100000


Output

742202979
#include <stdio.h>

const int K = 1e5+5;
const int mod = 1e9+7;

long long fastexp(int b,int e){
    if(e==0) return 1;
    long long ans = fastexp(b,e/2);
    ans = (ans*ans)%mod;
    if(e%2==1) ans=(ans*b)%mod;
    return ans;
}

long long pot[K];

int main(){
    int n,k;
    long long ans=0;
    scanf("%d %d", &n,&k);
    for(int i = k;i>0;i--){
        pot[i] = fastexp(k/i,n);
        for(int j = 2;i*j<=k;j++){
            pot[i]-=pot[i*j];
        }
        while(pot[i]<0) pot[i]+=mod;
        ans = (ans+(i*pot[i])%mod)%mod;
    }
    printf("%lld\n", ans);
}