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<bits/stdc++.h>
using namespace std;
#define int long long
const int MAXK=1e5+69,MOD=1e9+7;
int n,k,ans;
int cnt[MAXK];
int luythua(int x,int y){
    if(y==0)return 1;
    if(y==1)return x;
    int k=luythua(x,y/2);
    return k*k%MOD*luythua(x,y&1)%MOD;
}
signed main(){
    cin>>n>>k;
    for(int i=k;i>=1;i--){
        cnt[i]=luythua(k/i,n);
        for(int j=i*2;j<=k;j+=i)cnt[i]=(cnt[i]-cnt[j]+MOD)%MOD;
        ans=(ans+cnt[i]*i%MOD)%MOD;
    }
    cout<<ans;
}