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
//E
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 1e5+10;
const int mod = 1e9+7;
ll Pow(ll x,ll d){
	ll tmp = 1;
	if(!d)return 1;
	ll a = Pow(x,d/2);
	tmp = a*a%mod;
	if(d%2)tmp = tmp*x%mod;
	return tmp;
}
ll f[maxn];
int main(){
	ll ans = 0;
	int n,k;
	cin >> n >> k;
	for(int i = k;i >= 1;i--){
		ll x = k/i;
		f[i] = Pow(x,n);	
		for(int j = i+i;j <= k;j+=i)f[i] = (f[i] - f[j] + mod)%mod;
		ans = (ans + f[i]*i)%mod;
	}
	cout << ans;
	return 0;
}
