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;
long long n,k,m=1e9+7,ans,i,q,a[100000009],ans1,ans3,s;
long long axar(long long p,long long q)
{
	if(q==1) return p;
	long long w=axar(p,q/2);
	if(q%2==1)
	{
		return ((w*w)%m*p)%m;
	}
	if(q%2==0)
	{
		return (w*w)%m;
	}
}
int main()
{
	cin>>n>>k;
	for(i=k;i>=1;i--)
	{
		q=i;
		
		while(q<=k)
		{
			ans1+=a[q]%m;
			q+=i;
			ans1=(ans1+m)%m;
		}
		a[i]=(axar(k/i,n)-ans1)%m;
		ans1=0;
		a[i]=(a[i]+m)%m;
	}
	for(i=1;i<=k;i++)
	{
		ans3+=i*a[i]%m;
		ans3=(ans3+m)%m;
	}
	cout<<ans3;
}