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 m = 1000000007;
int n, k;
long a[100001];

long mpow(long b, long e) {
  if (e == 0) return 1;
  if (e % 2 == 1) return b * mpow(b, e - 1) % m;
  long t = mpow(b, e / 2);
  return t * t % m;
}

int main() {
  cin >> n >> k;
  for (int i = 1; i <= k; ++i) {
    a[i] = mpow(k / i, n);
  }
  
  for (int i = k; i >= 1; --i) {
    for (int j = 2 * i; j <= k; j += i) {
      a[i] = (a[i] + m - a[j]) % m;
    }
  }
  
  long sum = 0;
  for (int i = 1; i <= k; ++i) {
    sum = (sum + a[i] * i) % m;
  }
  cout << sum << endl;
}