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>
#include <iostream>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long ll;
ll n,k,ans;
ll sum[1000005],mod=1000000007ll;
ll pow1(ll x,ll y){
	ll a=1,b=x;while(y){if(y&1)a=(a*b)%mod;b=(b*b)%mod;y>>=1;}return a;
}
int main(){
    cin>>n>>k;
    for(int i=k;i>=1;i--){
		sum[i]=pow1(k/i,n);
		for(int j=2;i*j<=k;j++){
			sum[i]=(sum[i]-sum[i*j]+mod)%mod;
		}
		ans=(ans+i*sum[i])%mod;
	}
	cout<<ans;
	//system("pause");
    return 0;
}
