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 int MOD = 1000000007;
int n, k;
ll cnt[100100];

ll lgput(ll x, ll y){
    if (x < 0) return 0;
    ll ans = 1;
    while (y){
        if (y & 1) ans = (ans * x) % MOD;
        x = (x * x) % MOD;
        y /= 2;
    }
    return ans;
}

int main(){
    cin >> n >> k;
    ll ans = 0;
    for (int i=k; i; i--){
        cnt[i] = lgput(k / i, n);
        for (int j=i+i; j<=k; j+=i){
            cnt[i] = (cnt[i] - cnt[j] + MOD) % MOD;
        }
        ans = (ans + i * cnt[i]) % MOD;
    }
    cout << ans;
    return 0;
}
