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;

const int mod = 1e9 + 7;
const int N = 1e5 + 3;

int n, k;
long long ar[N];

int bin_pow(int a, int n) {
    int ret = 1;
    while (n) {
        if (n & 1)
            ret = (ret * 1ll * a) % mod;
        a = (a * 1ll * a) % mod;
        n >>= 1;
    }
    return ret;
}

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

    long long ans = 0;
    for (int i = k; i >= 1; i--) {
        ar[i] = bin_pow(k / i, n);
        for (int j = i + i; j <= k; j += i)
            ar[i] = (ar[i] - ar[j] + mod) % mod;
        ans = (ans + (ar[i] * i)) % mod;
    }

    cout << ans << endl;
}
