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;
typedef long long ll;
const int N=1e5+5,mod=1e9+7;
ll ksm(ll a,ll b){
	ll ans=1;
	while(b){
		if(b&1) ans=ans*a%mod;
		a=a*a%mod;
		b>>=1;
	}
	return ans;
}
ll f[N],ans=0;
int main(){	
	int n,k;
	scanf("%d%d",&n,&k);
	for(int i=k;i>=1;i--){
		f[i]=ksm(k/i,n);
		for(int j=i+i;j<=k;j+=i)
			f[i]=(f[i]-f[j]+mod)%mod;
		ans=(ans+f[i]*i)%mod; 
	}
	printf("%lld\n",ans);
	return 0;
} 