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<algorithm>
#include<string>
using namespace std;
typedef long long ll;

ll Pow(ll x, ll n)
{
  if(n == 0) return 1;
  if(n % 2 == 0) return Pow(x*x % 1000000007, n/2);
  else return x * Pow(x,n-1) % 1000000007;
}

ll n,k;
ll gcd[100005];
ll sum;

int main()
{
	cin>>n>>k;
	for(ll i=1;i<=k;i++)
	{
		gcd[i]=Pow(k/i,n);
	}
	for(ll i=k/2;i>0;i--)
	{
		for(ll j=2*i;j<=k;j+=i)
		{
			gcd[i]-=gcd[j];
		}
	}
	for(ll i=1;i<=k;i++)
	{
		gcd[i]=i*gcd[i]%1000000007;
		sum+=gcd[i]%1000000007;
	}
	
	cout<<sum%1000000007;
	return 0;
}