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 int long long
using namespace std;
constexpr int mod=1e9+7;
int modpow(int x,int n){
    int ret=1;
    while(n){
        if(n&1)
            (ret*=x)%=mod;
        (x*=x)%=mod;
        n>>=1;
    }
    return ret;
}
signed main(){
    int n,k;
    cin>>n>>k;
    int a[100001];
    for(int i=1;i<=k;i++)
        a[i]=modpow(k/i,n);
    for(int i=k;i>0;i--)
        for(int j=2*i;j<=k;j+=i)
            (a[i]+=mod-a[j])%=mod;
    int sum=0;
    for(int i=1;i<=k;i++)
        (sum+=i*a[i])%=mod;
    cout<<sum<<endl;
}