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;
int64_t l=1000000007;
int64_t pow(int64_t a,int64_t b) {
  int64_t c;
  if(b==0) return 1;
  else {
    c=(((pow(a,b/2)+l)%l)*((pow(a,b/2)+l)%l)+l)%l;
    if(b%2==1) c=(c*a+l)%l;
    return (c+l)%l;
  }
}
int main() {
  int64_t n,k,s,i,j,m;
  cin>>n>>k;
  vector<int64_t> c(k+1);
  s=0;
  for(i=k;i>0;i--){
    m=k/i;
    c.at(i)=(pow(m,n)+l)%l;
    for(j=2;j<=m;j++) c.at(i)=(c.at(i)-c.at(i*j)+l)%l;
    s=(s+i*c.at(i)+l)%l;
  }
  cout<<s<<endl;
}