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;
constexpr int N = 1e5 + 5;
constexpr int MOD = 1e9 + 7;

LL qpow(int x, int y){
    LL ans = 1;
    while (y){
        if (y & 1) ans = 1LL * ans * x % MOD;
        y >>= 1;
        x = 1LL * x * x % MOD;
    }
    return ans;
}

LL n, k, x[N];
int main(){
    cin >> n >> k;
    LL ans = 0;
    for (int i = k; i >= 1; -- i){
        x[i] = qpow(k / i, n);
        for (int j = 2 * i; j <= k; j += i) x[i] -= x[j];
        ans = (ans + (1LL * i * x[i]) % MOD)%MOD;
    }
    cout << (ans + MOD) % MOD << endl;
    return 0;
}
