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;
#define ll long long
#define all(V) V.begin(),V.end()
const ll MOD = 1000000007;

int main() {
	int N, K;
	cin >> N >> K;
	vector<ll> A(N);
	for (int i = 0;i < N;i++) {
		cin >> A[i];
	}
	sort(all(A));
	int l = 0, r = N - 1;
	if (K % 2) {
		if (A[N - 1] < 0) {
			ll ans = 1;
			for (int i = 0;i < K;i++) {
				ans *= A[N - 1 - i];
				ans %= MOD;
			}
			if (ans < 0)ans += MOD;
			cout << ans << endl;
			return 0;
		}
		else {
			r--, K--;
		}
	}
	ll lv = 0, rv = 0;
	while (K) {
		lv = A[l] * A[l + 1];
		rv = A[r] * A[r - 1];
		if (lv > rv) {
			l += 2;
		}
		else {
			r -= 2;
		}
		K -= 2;
	}
	ll f = 1;
	for (int i = 0;i < l;i++) {
		f *= A[i];
		f %= MOD;
	}
	for (int i = r + 1;i < N;i++) {
		f *= A[i];
		f %= MOD;
	}
	if (f < 0)f += MOD;
	cout << f << endl;
}