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;
int n, m, c, i, j, k, x, y, mo=1e9+7;
long long a[200005];
int cmp(int a, int b){
	return abs(a) < abs(b);
}
int main(){
	scanf("%d%d", &c, &k);
	for(i=1; i<=c; i++){
		scanf("%lld", &a[i]);
		if(a[i] < 0) x++;
		if(a[i] > 0) y++;
	}
	n = k;
	while(x >= 2 && n >= 2) x -= 2, n -= 2;
	if(y >= n){
		sort(a+1, a+c+1);
		n = c;
		if(k&1) m = a[n--], k--;
		else m = 1;
		for(i=1, j=n; k>0; k-=2){
			if(a[i]*a[i+1] > a[j]*a[j-1]){
				m = m * (a[i]*a[i+1]%mo) % mo;
				i += 2;
			}
			else{
				m = m * (a[j]*a[j-1]%mo) % mo;
				j -= 2;
			}
		}
		printf("%d\n", m);
	}
	else{
		sort(a+1, a+c+1, cmp);
		for(m=i=1; i<=k; i++){
			m = m * a[i] % mo;
		}
		printf("%d\n", (m+mo)%mo);
	}
	return 0;
}