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 <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;

#define mod 1000000007

int main() {
	int n, k;
	long long a[200002];
	scanf("%d%d", &n, &k);
	for (int i = 0; i < n; i++)
		scanf("%lld", &a[i]);
	sort(a, a + n);
	int l = 0, r = n - 1, w = 1;
	long long ans = 1;
	if (k & 1) {
		ans = a[r--];
		k--;
		w = (ans < 0 ? -1 : 1);
	}
	while (k) {
		long long x = a[l] * a[l + 1], y = a[r] * a[r - 1];
		if (x * w > y* w)
			ans = (ans * (x % mod)) % mod, l += 2;
		else
			ans = (ans * (y % mod)) % mod, r -= 2;
		k -= 2;
	}
	printf("%lld\n", (ans % mod + mod) % mod);
}
