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 N = 100005;
const int MOD = 1000000007;

int power(int x, int y) {
  int ret = 1;
  for (; y; y >>= 1) {
    if (y & 1) ret = 1LL * ret * x % MOD;
    x = 1LL * x * x % MOD;
  }

  return ret;
}

int g[N];

int main() {
  int n, k;
  scanf("%d %d", &n, &k);

  int ans = 0;
  for (int i = 1; i <= k; ++i) {
    g[i] += i;
    for (int j = i*2; j <= k; j += i) {
      g[j] -= g[i];
    }

    ans = (ans + 1LL * power(k/i, n) * g[i]) % MOD;
  }

  printf("%d\n", ans);
  return 0;
}
