Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

* 1 \leq K \leq N \leq 2\times 10^5
* |A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:


N K
A_1 \ldots A_N


Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Examples

Input

4 2
1 2 -3 -4


Output

12


Input

4 3
-1 -2 -3 -4


Output

1000000001


Input

2 1
-1 1000000000


Output

1000000000


Input

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1


Output

999983200
#include<bits/stdc++.h>
using namespace std;
using ll = long long;

int n, k;
ll a[200200], ans = 1, mod = 1e9 + 7;

int main(){
	ios_base::sync_with_stdio(0);cin.tie(0);
	cin >> n >> k;
	for(int i=1;i<=n;i++) cin >> a[i];
	sort(a+1, a+1+n);
	
	int l = 1, r = n;
	if(k % 2) ans = a[r], r--, k--;
	while(k){
		k -= 2;
		ll x = a[l] * a[l+1] * (ans < 0 ? -1 : 1), y = a[r] * a[r-1] * (ans < 0 ? -1 : 1);
		if(x > y) ans = ans * a[l] % mod * a[l+1] % mod, l += 2;
		else ans = ans * a[r] % mod * a[r-1] % mod, r -= 2;
	}
	cout << (ans + mod) % mod;
}