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;

int64_t power(int64_t a, int64_t b) {
  if(b==0)
    return 1;
  int64_t c=power(a,b/2)%1000000007LL;
  if(b%2==0)
    return c*c%1000000007LL;
  else
    return a*c%1000000007LL*c%1000000007LL;
}

int main() {
  int64_t N, K;
  cin >> N >> K;
  vector<int64_t> x(K+1);
  int64_t s=0;
  for(int64_t i=K;i>=1;i--) {
    x.at(i)=(int64_t)power(K/i, N);
    for(int j=2;j<=K/i;j++)
      x.at(i) -= x.at(j*i);
    s += i*x.at(i);
  }
  cout << s%1000000007LL << endl;
}