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>
#define ll long long
const int K=1e5+5;
const int mod=1e9+7;
using namespace std;
ll dp[K];
ll quick_pow(ll x,ll y){
	ll res=1;
	while(y){
		if(y%2==1) res=(res*x)%mod;
		x=(x*x)%mod;
		y>>=1;
	}
	return res;
}
int main(){
	ll n,k; cin>>n>>k;
	for(int i=k;i>=1;i--){
		dp[i]=quick_pow(k/i,n);
		for(int j=2*i;j<=k;j+=i) dp[i]-=dp[j];
	}
	ll ans=0;
	for(int i=1;i<=k;i++)
		ans=(ans+(dp[i]*i)%mod)%mod;
	cout<<ans<<endl;
	return 0;
}
