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 <stdio.h>
#include <math.h>

int compare (const void * a, const void * b) {
  return ( *(long long int*)a - *(long long int*)b );
}

int main() {
    
    long long int n, k, v = 0;
    long long int lista1[200001];
    long long int lista2[200001];
    
    scanf("%d%d", &n, &k);
    
    for (long long int i = 0; i < n; ++i)
        scanf("%d", &lista1[i]);
    
    for (long long int i = 0; i < n; ++i)
        lista2[i] = lista1[i];
    
    qsort (lista2, n, sizeof(int), compare);
    
    long long int min = lista1[0];
    long long int max = lista2[0];
    
    for (long long int i = 1; i < k; ++i)
        min *= lista1[i];
    
    for (long long int i = 1; i < k; ++i)
        max *= lista2[i];
 
    if (min > max)
        max = min;
    
    int MOD = 1000000007;
    
    if (max > 0)
        printf("%d\n", 1000000007 - abs(max));
    else
        printf("%d\n", max);
    
    return 0;
}