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 int
const long mod=1e9+7;
using namespace std;
ll dp[1<<17];
ll power(ll a,ll b){return b?power(a*a%mod,b/2)*(b%2?a:1)%mod:1;}
int main()
{
	ll n,k;
	while(cin>>n>>k){
        ll rslt=0;
        for(ll i=k;i>=1;i--){
            dp[i]=power(k/i,n);
            for(ll j=i+i;j<=k;j+=i)
                dp[i]-=dp[j];
            rslt+=i*dp[i]%mod;
        }
        cout<<rslt%mod<<endl;
	}
  return 0;
}
