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,mo=1e9+7;
LL Power(LL a,int b){
	LL ans=1;
	while(b){
		if(b&1)(ans*=a)%=mo;
		(a*=a)%=mo,b>>=1;
	}
	return ans;
}
int f[N];
int main(){
	int n,k;scanf("%d%d",&n,&k);
	LL ans=0;
	for(int i=k;i;i--){
		f[i]=Power(k/i,n);
		for(int j=i*2;j<=k;j+=i)(f[i]-=f[j])%=mo;
		ans+=1ll*i*f[i]%mo;
	}
	printf("%lld",(ans%mo+mo)%mo);
	return 0;
}