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 PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
list($N, $K) = array_map(function ($n) {
    return (int)$n;
}, explode(' ', fgets(STDIN)));

$A = array_map(function ($n) {
    return (int)$n;
}, explode(' ', fgets(STDIN)));

sort($A);

$ans = 1;
$n = 0;
$mod = 1000000007;

while ($n !== $K) {
    $len = count($A);
    if (isset($A[$len-2]) && $A[$len-2] >= 0) {
        if ($A[0] * $A[1] > $A[$len-1] * $A[$len-2] && $n + 1 < $K) {
            $n += 2;
            $ans *= array_shift($A) * array_shift($A);
        } else {
            $n += 1;
            $ans *= array_pop($A);
        }
    } else {
        if ($A[$len-1] > 0 && $n + 1 < $K) {
            $n += 2;
            $ans *= array_shift($A) * array_shift($A);
        } else {
            $n += 1;
            $ans *= array_pop($A);
        }
    }
    $ans %= $mod;
}

echo $ans >= 0 ? $ans : $mod + $ans;