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;
typedef long long ll;
const int maxn=1e5+5;
const int mod=1e9+7;
ll kpow(ll a,ll b)
{
	ll ans=1;
	while(b)
	{
		if(b&1)ans=(ans*a)%mod;
		a=(a*a)%mod;
		b>>=1;
	}
	return ans;
}
int main()
{
	ll n,k,ans=0,cnt=0,s[maxn]={0};
	scanf("%lld%lld",&n,&k);
	for(ll i=k;i>=2;i--)
	{
		ll sum=k/i,pp=0;
		pp=kpow(sum,n);
		for(ll j=2;j<k;j++)
		{
			if(j*i>k)break;
			pp=(pp-s[i*j]+mod)%mod;
		}
		s[i]=pp;
		cnt=(cnt+pp)%mod;
		ans=(ans+pp*i)%mod;
	}
	ans=(ans+kpow(k,n)-cnt+mod)%mod;
	printf("%lld\n",ans);
}