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 <iostream>

using namespace std;

const int M = 1e9+7;

long long memo[100100];

long long mpow(long long a, int n)
{
  if (n % 2) return mpow(a, n-1)*a%M;
  if (not n) return 1;
  return mpow(a*a%M, n/2);
}

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