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;
typedef long long ll;

ll mod = 1e9+7;
ll memo[1<<17];
ll modPow(ll,ll,ll);
int main(){
    ll n,k,ans=0;
    cin >> n >> k;

    for(ll i = k; i >= 1; i--){
        memo[i]= modPow(k/i,n,mod);  //gcdがiになる個数
        
    
        for(ll j = 2*i; j <= k ; j = j + i){
            memo[i] -= memo[j];
        }
        ans += memo[i]*i%mod;
        
    }

    cout << ans%mod << endl;    

}


ll modPow(ll a,ll n,ll mod) {
  if (n == 1) return a % mod;
  if (n % 2 == 1) return (a * modPow(a, n - 1, mod)) % mod;
  ll t = modPow(a, n / 2, mod);
  return (t * t) % mod;
}