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 N=1e5+10;
const int mod=1e9+7;
ll f[N];
ll n,k;
ll qpow(ll x,ll y) {
	ll s=1;
	while (y) {
		if (y&1) s=(s*x)%mod;
		x=(x*x)%mod;
		y>>=1;	
	}
	return s;
}
int main() {
	ll i,j,ans=0;
	cin>>n>>k;
	for (i=k;i>=1;i--) {
		f[i]=qpow(k/i,n);
		for (j=i+i;j<=k;j+=i)
			f[i]=(f[i]-f[j]+mod)%mod;
		ans=(ans+f[i]*i%mod)%mod;
	}
	cout<<ans<<endl;
	return 0;
}