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;

#define REP(i,n) for(int i = 0; i < (int)(n); i++)

const uint64_t mod = 1000000007;

uint64_t po(uint64_t d, uint64_t n){
  if(n == 1) return d;
  if(n == 0) return 1;
  uint64_t p = po(d, n >> 1);
  p = p * p % mod;
  if(n & 1) p = p * d % mod;
  return p;
}

int main(){
  uint64_t r = 0;
  int n, k;
  cin >> n >> k;
  vector<int> a(k + 1);
  for(int m = k + 1; --m; ){
    uint64_t p = po(k / m, n);
    for(int v = 2; m * v <= k; ++v){
      p = (p + mod - a[m * v]) % mod;
    }
    a[m] = p;
    r = (r + p * m) % mod;
  }
  cout << r << endl;
  return 0;
}