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<iostream>
#include<cstdio>
using namespace std;
const int mod=1e9+7;
int n,k,ans,f[202019];
int fpow(int x,int y){
	int res=1;
	for(;y;y>>=1,x=1ll*x*x%mod)
		if(y&1)res=1ll*res*x%mod;
	return res;
}
int main()
{
	scanf("%d%d",&n,&k);
	for(int i=k;i>=1;i--){
		f[i]=fpow(k/i,n);
		for(int j=i+i;j<=k;j+=i)
			f[i]=(f[i]-f[j])%mod;
		ans=(ans+1ll*f[i]*i%mod)%mod;
	} cout<<(ans+mod)%mod<<endl;
	return 0;
}