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;
const int N=1e5+10;
const int MOD=1e9+7;
typedef long long ll;
ll qpow(ll a,ll b){
    ll ans=1;
    while(b){
        if(b%2){
            ans=(ans*(a%MOD))%MOD;
        }
        b/=2;
        a=a*a%MOD;
    }
    return ans;
}
ll f[N];
int main()
{
    //cout<<qpow(2,4);
    ll n,k;
    cin >>n>>k;
    ll ans=0;
    for(int i=k;i>=1;i--){
            f[i]=qpow(k/i,n);
        for(int j=i*2;j<=k;j+=i){
            f[i]-=f[j];
        }
        ans=(ans+i*f[i]%MOD)%MOD;
    }
    cout<<(ans+MOD)%MOD<<endl;
}
