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 int mod=1e9+7;
long long ans,f[100006];

long long poww(int a,int b)
{
	long long ans=1,tmp=a;
	while(b) {if(b&1) ans=ans*tmp%mod;tmp=tmp*tmp%mod;b>>=1;}
	return ans;
}

int main()
{
	int n,k;
	scanf("%d%d",&n,&k);
//	ans=poww(k,n);
	for(int i=k;i>=1;--i) {
		f[i]=poww((k/i),n);
		for(int j=2;i*j<=k;++j) {
			f[i]-=f[i*j];
			f[i]%=mod;
		}
		(f[i]+=mod)%=mod;
	}
	for(int i=1;i<=k;++i) {
		ans+=i*f[i]%mod;
		ans%=mod;
	}
	printf("%lld",ans);
}