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;

// macro
#define rep(i,n) for(i=0;i<n;i++)
#define ll long long
#define all(v) v.begin(), v.end()

// code starts
#define MOD 1000000007

ll pow(ll a, ll x)
{
	ll left=x;
	ll ret=1;
	ll ks=a;
	while(left>0)
	{
		if(left%2==1)ret=ret*ks%MOD;
		left/=2;
		ks=ks*ks%MOD;
	}
	return ret;
}

int main()
{
	ll n,k;cin>>n>>k;
	vector<ll> count(k+1,0);
	int i,j;
	for(i=k;i>=1;i--)
	{
		count[i]=pow(k/i,n);
		for(j=i*2;j<=k;j+=i)
		{
			count[i]+=MOD-count[j];
			count[i]%=MOD;
		}
	}
	ll ans=0;
	for(i=1;i<=k;i++)
	{
		ans=ans+count[i]*i%MOD;
		ans%=MOD;
	}
	cout<<ans<<endl;
}
