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;

const int MOD = 1e9 + 7;

int main() {
	int n, k;
	cin >> n >> k;
	vector<int> a(n);
	int negs = 0;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
		if (a[i] < 0)
			negs++;
	}
	sort(a.begin(), a.end(), greater<int>());
	int resp = 1;
	for (int i = 0, esq = 0, dir = n - 1; i < k; i++) {
		if (negs > 1 && (k - i) > 1 && (a[dir] * 1ll * a[dir - 1]) > (a[esq] * 1ll * a[esq + 1])) {
			resp = (resp * 1ll * a[dir]) % MOD;
			resp = (resp * 1ll * a[dir - 1]) % MOD;
			dir -= 2;
			negs -= 2;
			i++;
		} else {
			resp = (resp * 1ll * a[esq]) % MOD;
			esq++;
		}
	}
	if (resp < 0) {
		resp = 1;
		for (int i = 0; i < n; i++)
			a[i] = abs(a[i]);
		sort(a.begin(), a.end());
		for (int i = 0; i < k; i++) {
			resp = (resp * 1ll * a[i]) % MOD;
		}
		resp *= -1;
		resp = MOD - abs(resp);
	}
	cout << resp % MOD << endl;
	return 0;
}