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;
using ll = long long;
const ll MOD = 1e9+7;

ll modpow(ll m, ll n){
  if(n == 0) return 1;
  else if(n % 2 == 0) return modpow(m * m % MOD, n/2);
  else{
    return modpow(m, n - 1) * m % MOD;
  }
}

int main(){
    int n, k; scanf("%d %d", &n, &k);
    ll ans = 0;
    vector<ll> data(k + 1, 0);

    for(int g = k; g >= 1; g--){
        ll cnt = modpow(k/g, n);
        for(int i = g; i <= k; i += g){
            (cnt += -data[i] + MOD) %= MOD;
        }
        data[g] = cnt;
        (ans += (cnt * g)%MOD) %= MOD;
    }

    printf("%lld\n", ans);
}