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 int ll;
ll mod = 1000000007;
ll modular_pow(ll a,ll b){
	if(b == 0)
		return 1LL;
	ll x = modular_pow(a,b/2) % mod;
	x = (x * x) % mod;
	if(b & 1)
		return (a * x)%mod;
	return x;
}

int main(){
	ll n,k;
	cin>>n>>k;

	ll dp[k+1];

	ll sum = 0;
	for(ll i =1;i <= k;i++){
		dp[i] = modular_pow(k/i,n);

	}

	for(ll i = k;i>=1;i--){
		for(ll j = i * 2;j<=k ;j+=i){
			dp[i] = (dp[i] - dp[j] + mod)%mod;
			dp[i] = (dp[i] + mod);
		}
		sum = (sum + (dp[i] * i) %mod)%mod;
	}

	
	
	cout<<sum;
	cout<<"\n";

	return 0;




}