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 ll mod=1e9+7;
ll dp[100005];
ll qpow(ll a,ll b)
{
	if(b==0) return 1;
	ll c=qpow(a,b/2);
	if(b%2==0) return c*c%mod;
	else return c*c%mod*a%mod;
}
int main()
{
	ll n,k;
	scanf("%lld%lld",&n,&k);
	ll sum=0;
	for(ll i=k;i>0;i--)
	{
		dp[i]=(qpow(k/i,n))%mod;
		for(ll j=i*2;j<=k;j+=i) dp[i]=(dp[i]-dp[j]+mod)%mod;
		sum=(sum+dp[i]*i)%mod;
	}
	printf("%lld",sum);
}