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;

const long long mod=1e9+7;
int n, k;
long long a[100002];
long long ans=0;

long long modpow(long long x, int y){
	long long ret=1;
	for (;y>0;y>>=1){
		if (y&1){
			ret*=x;
			ret%=mod;
		}
		x*=x;
		x%=mod;
	}
	return ret;
}

int main(){
	cin >> n >> k;
	for (int i=k;i>0;i--){
		a[i]=modpow(k/i,n);
		for (int j=i+i;j<=k;j+=i){
			a[i]-=a[j];
			a[i]%=mod;
			a[i]+=mod;
			a[i]%=mod;
		}
		ans+=(i*a[i])%mod;
		ans%=mod;
	}
	cout << ans << "\n";
}	