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>
#define MOD 1000000007
#define ll long long
#define mp make_pair
#define pb push_back 
using namespace std;
ll raise(ll a, ll b){
	ll ans = 1;
	while(b){
		if(b & 1){
			ans = (ans * a) % MOD;
		}
		b /= 2;
		a = (a * a) % MOD;
	}
	return ans;
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	ll n, k;
	cin >> n >> k;
	vector<ll> dp(k + 1);
	ll ans = 0;
	for(int i = k; i >= 1; i--){
		ll cur = raise(k / i, n);
		for(int j = 2 * i; j <= k; j += i){
			cur = (cur - dp[j] + MOD) % MOD;
		}
		dp[i] = cur;
		ans = (ans + (i * cur) % MOD) % MOD;
	}
	cout << ans << '\n';

}