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 <iostream>
#include <algorithm>
using namespace std;

long long n, k, m = 1;
const long long M = 1e9 + 7;
long long a[200000];

int main()
{
	cin >> n >> k;

	for (int i = 0; i < n; i++)
		cin >> a[i];

	sort(a, a + n);

	if (a[n - 1] <= 0 && k % 2 == 1) {
		for (int i = 0; i < k; i++)
			m = m * (a[n - 1 - i] + M) % M;
	}
	else {
		int i = 0, j = 0, l = n - 1;

		while (i < k) {
			if (i == k - 1 || a[j] * a[j + 1] < a[l] * a[l - 1]) {
				m = m * a[l] % M;
				l--;
				i++;
			}
			else {
				m = m * (a[j] + M) % M * (a[j + 1] + M) % M;
				j += 2;
				i += 2;
			}
		}
	}

	cout << m << endl;
}
