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>
typedef long long ll;
const int mod=1e9+7;
const int N=1e5+5;

ll n,k;
ll ans;
ll f[N];
ll po(ll a,ll b)
{
	ll ans=1;
	while(b)
	{
		if(b&1) ans=ans*a%mod;
		b>>=1;
		a=a*a%mod;
	}
	return ans;
}

int main()
{
	// freopen("test.in","r",stdin);
	// scanf("%d",&T);
	// while(T--)
	// {
	scanf("%lld%lld",&n,&k);
	ll ans=0;
	for(ll i=k;i;i--)
	{
		f[i]=po(k/i,n);
		for(ll j=i+i;j<=k;j+=i)
			f[i]-=f[j];
		f[i]%=mod;
		f[i]+=mod;
		f[i]%=mod;
		ans+=f[i]*i%mod;
		ans%=mod;
	}
	printf("%lld\n",ans);
	// }
	return 0;
}
