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 int long long
const int MOD=1e9+7;
int pw(int n,int k){
  assert(k>=0);
  int res=1;
  while(k){
    if(k&1)(res*=n)%=MOD;
    (n*=n)%=MOD;
    k>>=1;
  }
  return res;
}

int F[123456],ans;

signed main(){
  int n,k;cin>>n>>k;
  for(int i=1;i<=k;i++){
    (F[i]+=i)%=MOD;
    for(int j=i+i;j<=k;j+=i)F[j]+=MOD-F[i];
  }
  for(int i=1;i<=k;i++)ans+=pw(k/i,n)*(MOD+F[i])%MOD;
  cout<<ans%MOD<<endl;
}
