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;
#define int long long
const int maxm=1e5+5;
const int mod=1e9+7;
int f[maxm];
int ppow(int a,int b,int mod){
    int ans=1%mod;a%=mod;
    while(b){
        if(b&1)ans=ans*a%mod;
        a=a*a%mod;
        b>>=1;
    }
    return ans;
}
signed main(){
    int n,k;cin>>n>>k;
    int ans=0;
    for(int i=k;i>=1;i--){//枚举gcd
        f[i]=ppow(k/i,n,mod);
        for(int j=i+i;j<=k;j+=i){
            f[i]=(f[i]-f[j]+mod)%mod;
        }
        ans=(ans+f[i]*i%mod)%mod;
    }
    cout<<ans<<endl;
    return 0;
}
