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>
#include<cmath>
#include<cstdio>
#include<algorithm>
#include<queue>
#include<cstring>
#define ll long long
using namespace std;

const ll mod=1e9+7;

ll ksm(ll b,ll p)
{
	ll ans=1;
	while(p>0)
    {
        if(p%2==1)
            ans=(ans*b)%mod;
        b=(b*b)%mod;
        p/=2;
    }
    return ans;
}

ll f[500010],anss;

int main()
{
	int n,k;
	cin>>n>>k;
	for(ll i=k;i>=1;i--)
	{
		ll cnt=k/i;
		f[i]=ksm(cnt,n);
		for(ll j=2*i;j<=k;j+=i)
		{
			f[i]=(f[i]+mod-f[j])%mod;
		}
	}
	for(ll i=1;i<=k;i++)
	{
		anss+=f[i]*i;
		anss%=mod;
	}
	cout<<anss;
}