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;
typedef long long ll;
const ll MOD = 1000000007;

ll modpow(ll a, ll n){
    ll res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % MOD;
        a = a * a % MOD;
        n >>= 1;
    }
    return res;
}
 
int main(){
    ll N, K;
    cin >> N >> K;

    ll ans = 0;
    ll num[K+1];
    for(ll i=K;i>=1;i--){
        num[i] = modpow(K/i, N);
        for(ll j=2;i*j<=K;j++)
            num[i] = (num[i] - num[i*j] + MOD) % MOD;
        ans = (ans + i*num[i]) % MOD;
    }

    cout << ans << endl;

}