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>
#define mod 1000000007
using namespace std;
typedef long long ll;
ll exp(ll a,ll b)
{
	if(b==0)
	 return 1;
	if(b%2==0)
	 return exp(a*a%mod,b/2);
	return a*exp(a*a%mod,(b-1)/2)%mod;
}
int main()
{
	ll n,k;
	cin>>n>>k;
	vector<ll>dp(k+1);
	ll ans=0;
	for(ll i=k; i>=1; i--)
	{
		ll temp=exp(k/i,n);
		for(ll x=2; i*x<=k; x++)
		{
			temp=(temp-dp[i*x]+mod)%mod;
		}
	    dp[i]=temp;
	    ans=(ans+i*dp[i])%mod;
	}
	cout<<ans;
	return 0;
}