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++)
using ll = long long;
const ll mod = 1e9+7;

ll Pow(ll x, ll n){
  if(n == 0) return 1;
  if(n % 2 == 0) return Pow(x*x % mod, n/2);
  else return x * Pow(x,n-1) % mod;
}

int main(){
  ll n, k;
  cin >> n >> k;
  vector<ll> p(k+1,0);
  for(ll i = k; i >= 1; i--) {
    p[i] += Pow(k/i,n);
    for(int j = 2*i; j <= k; j += i) {
      (p[i] -= p[j]) %= mod;
    }
  }
  ll ans = 0;
  for(ll i = 1; i <= k; i++) (ans += i * p[i]) %= mod;
  cout << (ans + mod) % mod << endl; 
  return 0;
}
