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>

using ll=long long int;

constexpr ll mod = 1e9+7;
constexpr int MAX_K = 1e5;


int n,k;

ll g[MAX_K];

//n乗
ll pow(ll x){

    ll res=1;

    for(int i=0;i<30;++i){
        if((1<<i)&n)
            res=res*x%mod;
        x=x*x%mod;
    }

    return res;
}

int main(){

    std::cin>>n>>k;

    for(int i=k;i>=1;--i){
        g[i]=pow(k/i);
        for(int j=2;j*i<=k;++j)
            g[i]=(g[i]-g[j*i])%mod;
    }

    ll ans=0;

    for(ll i=1;i<=k;++i)
        ans=(ans+g[i]*i)%mod;

    std::cout<<ans<<std::endl;

    return 0;
}