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;
using ll =long long;
ll n,k;
ll ans;
ll dp[1<<17];
const ll mod = 1e9+7;
ll qpow(ll x,ll n)
{
    ll res =1;
    while(n>0)
    {
        if(n&1) res=res*x%mod;
        x=x*x%mod;
        n>>=1;
    }
    return res;
}
int main(){
	cin>>n>>k;
	for(ll i=k;i>0;i--){
		dp[i]=qpow(k/i , n);
		for(ll j=i+i;j<=k;j+=i){
			dp[i]-=dp[j];  //+mod%mod防溢出 
		}
	}
	for(ll i=1;i<=k;i++) ans=(ans+dp[i]*i)%mod;
	cout<<ans%mod<<endl;
	return 0;
}