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;

long long solve(vector<int>& a, int n, int k) {
	long long res = 1;
	
	if (a[n-1] == 0 && k%2) {
		return 0;
	}
	
	if (a[n-1] < 0 && k%2) {
		for (int i = n-1; i >= n-k; i--) {
			res = (res*a[i]) % mod;
		}
		return (res + mod) % mod;
	}
	
	if (a[n-1] > 0 && k%2) {
		res = a[n-1];
		--n; --k;
	}
	
	// k is even
	k /= 2;
	int l = 0, r = n-1;
	while (k--) {
		long long left = 1LL * a[l] * a[l+1], right = 1LL * a[r] * a[r-1];
		if (left > right) {
			res = (res*(left%mod))%mod;
			l += 2;
		} else {
			res = (res*(right%mod))%mod;
			r -= 2;
		}
	}
	return (res + mod) % mod;
}

int main() {
	int n, k;
	cin >> n >> k;
	vector<int> a(n);
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}
	sort(a.begin(), a.end());
	
	cout << solve(a, n, k) << endl;
}