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 modulo 1000000007
#define mod(mod_x) ((((long long)mod_x)+modulo)%modulo)
#define Inf 1000000000

//aのb乗
int beki(int a,int b,int M = modulo){
	int x = 1;
	while(b!=0){
		if(b&1){
			x=((long long)x*a)%M;
		}
		a=((long long)a*a)%M;
		b>>=1;
	}
	return x;
}

int main() {
	
	int N,K;
	cin>>N>>K;
	
	vector<int> cnt(K+1,0);
	
	for(int i=K;i>=1;i--){
		cnt[i] = beki(K/i,N);
		for(int j=2*i;j<=K;j+=i){
			cnt[i] = mod(cnt[i] - cnt[j]);
		}
	}
	
	int ans = 0;
	for(int i=1;i<=K;i++){
		ans = mod(ans + mod(i*cnt[i]));
	}
	
	cout<<ans<<endl;
	
    return 0;
}
