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;
const int maxN=1e5+10;
const long long MOD=1e9+7;
int n;
long long k;
long long ans[maxN];
long long res=0LL;
long long fast_mi(long long a,int p)
{
	if(p==0)
	{
		return 1LL;
	}
	long long tmp=fast_mi(a,p>>1);
	tmp=tmp*tmp%MOD;
	if(p&1)
	{
		tmp=tmp*a%MOD;
	}
	return tmp;
}
int main()
{
	cin>>n>>k;
	for(long long x=k;x>=1LL;x--)
	{
		long long multi_num=k/x;
		long long num=fast_mi(multi_num,n);
		for(int i=x+x;i<=k;i+=x)
		{
			num=(num-ans[i]+MOD)%MOD;
		}
		ans[x]=num;
		res=(res+num*x)%MOD;
	}
	cout<<res<<endl;
	return 0;
}
