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;
int main(){
  int n,k;
  cin>>n>>k;
  int p=1000000007;
  vector<int64_t> e(k+1,1);
  for(int i=0;i<=k;i++){
    int x=n;
    vector<bool> b;
    while(x>0){
      b.push_back(x%2==1);
      x/=2;
    }
    for(int d=(int)b.size()-1;d>=0;d--){
      e.at(i)=e.at(i)*e.at(i)%p;
      if(b.at(d))
        e.at(i)=e.at(i)*i%p;
    }
  }
  vector<int64_t> c(k+1,0);
  int64_t s=0;
  for(int i=k;i>=1;i--){
    c.at(i)=e.at(k/i);
    for(int j=2;i*j<=k;j++)
      c.at(i)=(c.at(i)-c.at(i*j)+p)%p;
    s=(s+c.at(i)*i)%p;
  }
  cout<<s<<endl;
}