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 read() {
	int x; scanf("%d", &x); return x;	
}
const int maxn = 2e5 + 10;
const int INF = 1e9;
int n, m, k, a[maxn];
int mod = 1e9 + 7;
using namespace std;

int main() {
	n = read(), k = read();
	for (int i = 1; i <= n; ++i) a[i] = read();
	sort(a + 1, a + 1 + n);
	int l = 1, r = n - k + 1;
	while (l < r && r <= n - 1) {
		if (1ll * a[l] * a[l + 1] >= 1ll * a[r] * a[r + 1]) l += 2, r += 2;
		else break;
	}
	if (a[n] < 0 && k & 1) l = 1, r = n - k + 1;
	int ans = 1;
	for (int i = 1; i < l; ++i) ans = 1ll * ans * ((a[i] + mod) % mod) % mod;
	for (int i = r; i <= n; ++i) ans = 1ll * ans * ((a[i] + mod) % mod) % mod;
	cout << ans << endl;
	return 0;	
}
