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 <iostream>
#define int64 long long int
using namespace std;
const int mod = 1e9+7 , MAX = 400009 ;
int64 cnt[MAX] ;
int expo(int a,int n){
    int ret=1;
    while(n>0){
        if(n&1)  ret = (1LL * ret * a)%mod ;
        a = (1LL *a * a)%mod ;
        n>>=1;
    }
    return ret;
}
int main(){
    int n , k  ;
    scanf("%d%d",&n,&k);
    int64 ret =0  ;
    for(int i=k;i;i--){
        cnt[i] = expo(k/i,n);
        for(int j=i+i;j<=k;j+=i){
            cnt[i] += mod-cnt[j];
            cnt[i] %= mod ;
        }
        ret += (1LL * i * cnt[i]);
        ret %= mod ;
    }
    printf("%lld\n",ret);
}