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
#define MAX 5000005
#define P ((ll)1e9+7)
using namespace std;

ll qpow(ll a, ll n){
    ll res = 1;
    while(n){
        if(n&1) res = res*a%P;
        a = a*a%P, n >>= 1;
    }
    return res;
}

int n, m;
ll f[MAX];

int main()
{
    cin >> n >> m;

    ll ans = 0;
    for(int i = m; i >= 1; i--){
        f[i] = qpow(m/i, n);
        ans = (ans + f[i]*i%P)%P;
        for(int j = 2; i*j <= m; j++){
            ans = (ans-f[i*j]*i%P+P)%P;
            f[i] -= f[i*j];
        }
    }
    cout << ans << endl;

    return 0;
}
