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;
#define ll long long
const int mod=1e9+7;
const int N=1e5+5;
ll cnt[N];
ll n,k,ans;
ll pow(ll num)
{
	ll res=1,m=n;
	while(m>0){
	    if(m&1)
	    res=res*num%mod;
	    num=num*num%mod;
	    m>>=1;
	}
	return res;
}
int main()
{
	cin>>n>>k;
	for(ll i=k;i>=1;i--)
	{
	    cnt[i]=pow(k/i);
	    for(ll j=2;j*i<=k;j++)
		{
	        cnt[i]-=cnt[j*i];
	    }
	    ans+=(mod+(cnt[i]*i)%mod)%mod;
	    ans=(ans+mod)%mod;
	}
	cout<<ans<<endl;
	return 0;
}