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>
#define ll long long
using namespace std;
const int maxn=1e5+5;
const int mod=1e9+7;
ll f[maxn],n,k,ans;
ll fast(ll m,ll c){
    ll a=1;
    while(c)
	{
        if(c%2==1) a=a*m%mod;
        m=m*m%mod;
        c=c/2;
    }
    return a;
}
int main(){
    cin>>n>>k;
    for(int i=k;i>=1;i--)
	{
        f[i]=fast(k/i,n);
        for(int j=i*2;j<=k;j+=i)
            f[i]=(f[i]-f[j]+mod)%mod;
        ans=(ans+f[i]*i)%mod;
    }
    cout<<ans;
    return 0;
}