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>
#define ll long long
using namespace std;

const int MOD=1000000007;

ll modpow(ll x, ll n, ll mod) {
  if (n==0) return 1;
  ll res=modpow(x*x%mod, n/2, mod);
  if (n & 1) res=res*x%mod;
  return res;
}

int main() {
  int n,k; cin>>n>>k;
  vector<ll> dp(k+1);
  ll res=0;
  for (int i=k; i>=1; i--) {
    dp[i]=modpow(k/i, n, MOD);
    for (int j=i*2; j<=k; j+=i) dp[i]-=dp[j];
    dp[i]=(dp[i]%MOD+MOD)%MOD;
    res+=(i*dp[i])%MOD;
    res%=MOD;
  }
  cout<<res<<endl;
}
