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;
const long long md=1e9+7;
long long n,k,dp[202020],ans;
long long pw(long long x,long long y)
{
	long long nw=1ll;
	while(y)
	{
		if(y&1)
		{
			nw*=x;
			nw%=md;
		}
		y>>=1;
		x*=x;
		x%=md;
	}
	return nw;
}
int main()
{
	cin>>n>>k;
	for(int i=k;i>=1;i--)
	{
		long long mx=k/i,cnt=pw(mx,n);
		for(int j=i+i;j<=k;j+=i)
		{
			cnt=(cnt+md-dp[j])%md;
		}
		dp[i]=cnt;
		cnt*=(i*1ll);
		cnt%=md;
		ans+=cnt;
		ans%=md;
	}
	cout<<ans<<endl;
	return 0;
}