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;
using ll=long long;
constexpr ll mod=1000000007;

int N,K;
ll A[100001],res;

ll pw(ll x,int y){
	ll a=1;
	while(y){
		if(y&1)a=a*x%mod;
		x=x*x%mod;
		y/=2;
	}
	return a;
}

int main(){
	cin>>N>>K;
	for(int i=K;i>=1;i--){
		A[i]=pw(K/i,N);
		for(int j=i+i;j<=K;j+=i){
			A[i]=(A[i]+mod-A[j])%mod;
		}
		res+=A[i]*i;
		res%=mod;
	}
	cout<<res<<endl;
}
