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 ;
const int mod = 1e9 +7 , N = 1e5 + 5 ;
typedef long long ll ;
ll dp[N] ;
ll qmi(ll a, ll b)
{
  ll res =1 ;
  while(b)
   {
     if(b & 1) res = res * a % mod ;
     a = a * a % mod ;
     b >>= 1;
   }
   return res ;
}
int main()
{
  ll ans = 0 ;
  int n , k ;
  cin >> n >> k ;
  for(int i = k ;i >= 1;i --)
   {
     dp[i] = qmi(k / i , n) % mod ;
     for(int j = 2 * i ;j <= k ;j += i)
      dp[i] -= dp[j] , dp[i] = (dp[i] % mod + mod) % mod ;
     ans += i * dp[i] % mod , ans %= mod ;
   }
  cout << ans << endl ;
  return 0 ;
}
