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 ll long long
#define pb push_back
#define mp make_pair
#define mod 1000000007
ll power(ll x,ll y){
  ll res=1;
  while(y>0){
    if(y&1)
      res=(res*x)%mod;
    y=y/2;
    x=(x*x)%mod;
  }
  return res;
}
int main() {
  ll n,k;
  cin>>n>>k;
  ll ans=k;
  ll a[k+1];
  a[k]=1;
  ll i,j;
  for(i=k-1;i>=1;i--){
    a[i]=power(k/i,n);
    for(j=i+i;j<=k;j+=i){
     	a[i]=a[i]+mod-a[j];
     	if(a[i]>=mod)
       	a[i]=a[i]-mod;
  	}
    
  }
  for(int i=1;i<=k-1;i++){
    ans=ans+(1LL * a[i]*i);
    ans%=mod;
  }
  cout<<ans;         
  return 0;
}