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>

#define int         long long
const int m=1e9+7;
using namespace std;
int expo(int base,int exponent,int mod){
    int ans=1;
    while(exponent!=0){
        if(exponent&1) ans=(1LL*ans*base)%mod;
        base=(1LL*base*base)%mod;
        exponent>>=1;
    }
    return ans%mod;
}
int n,k,a[100005],ans;
void solve(){
	cin>>n>>k;
	for(int i=k;i>=1;i--){
		a[i]=k/i;
		a[i]=expo(a[i],n,m);
		for(int j=2*i;j<=k;j+=i){
			a[i]=(a[i]-a[j]+m)%m;
		}
		ans=(ans+a[i]*i)%m;
	}
	cout<<ans<<endl;
}

signed main(){
    ios::sync_with_stdio(false);
    
       solve();
    
    return 0;
}
