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;
ll k, n, c[100010] = {0};
vector<int> pri;
ll ans = 0;
const int M = 1e9 + 7;
int main() {
    cin >> n >> k;
    for(int i = k; i >= 1; i--) {
        ll a = k / i, s = 1;
        for(int j = n; j > 0; j >>= 1, a = a * a % M)
            if(j & 1) s = s * a % M;
        for(int j = 2 * i; j <= k; j += i) s -= c[j];
        c[i] = (s % M + M) % M;
        ans = (ans + c[i] * i) % M;
    }
    cout << ans;
}