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