Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <stack>
#include <set>
#include <map>
typedef long long int ll;
using namespace std;

const ll MOD = 1e9 + 7;

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	ll n, m, ans = 1;
	cin >> n >> m;
	ll a[n];
	for(ll i=0; i<n; i++)
		cin >> a[i];
	sort(a, a+n);
	for(ll i=n-1; i>n-1-m; i--){
		ans = (ans%MOD*a[i]%MOD)%MOD;
	}
	cout << ans;
	return 0;
}