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 ll N=1e5+7;
const ll MOD=1e9+7;
ll dp[N];
ll ksm(ll x,ll y){
	ll res=1;
	while(y){
		if(y&1) res=res*x%MOD;
		x=x*x%MOD;
		y>>=1;
	}
	return res%MOD;
}
int main(){
	ll n,k;
	cin>>n>>k;
	ll ans=0;
	for(ll i=k;i>=1;i--){
		dp[i]=ksm(k/i,n);
		for(ll j=2*i;j<=k;j+=i) dp[i]=(dp[i]-dp[j]+MOD)%MOD;
		ans=(ans+i*dp[i]+MOD)%MOD;
	}
	cout<<ans<<endl;
	return 0;
} 