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
#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
#define LL long long int
#define MOD 1000000007
LL mod_pow(int x,int n){
	LL X=x;
	LL ans=1;
	while (n>0){
		if((n&1)==1)ans=(ans*X)%MOD;
		X=(X*X)%MOD;
		n>>=1;
	}
	return ans;
}
int main() {
	int N,K;
	cin >>N>>K;
	vector<LL> gcd_exact(K+1);
	LL ans=0;
	for (int X = K; X > 0; X--){
		gcd_exact[X]=mod_pow(K/X,N);
		int s=2;
		while (s*X<=K)
		{
			gcd_exact[X]=(gcd_exact[X]+MOD-gcd_exact[s*X])%MOD;
			s++;
		}
		ans=(ans+X*gcd_exact[X])%MOD;
	}
	cout<<ans<<endl;
}