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 Python (3.8.2) (judge verdict: Wrong Answer)

def prod(l):
    r = 1
    mod = 10 ** 9 + 7
    for a in l:
        r = (r * a) % mod
    return r

def main():
    N, K = map(int, input().split())
    A = list(map(int, input().split()))
    P = [a for a in A if a >=0]
    M = [a for a in A if a < 0]
    PP, MM = len(P), len(M)
    P.sort(reverse=True)
    M.sort()
    k = 0
    p, m = 0, 0
    if PP == 0:
        if K % 2 == 0:
            return prod(M[:K])
        return prod(M[-K:])
    if P[0] == 0 and K % 2 == 1:
        return 0
    while p + m < K:
        if m == MM:
            p += 1
        elif p == PP:
            m += 1
        elif P[p] > -M[m]:
            p += 1
        else:
            m += 1
    if m % 2 != 0:
        if m == MM or p == 0:
            m -= 1
            p += 1
        elif p == PP or m == 0:
            m += 1
            p -= 1
        elif M[m - 1] * M[m] >= P[p - 1] * P[p]:
            m += 1
            p -= 1
        else:
            m -= 1
            p += 1
    if p < 0 or p > PP:
        return prod(M[-K:])
    return prod(P[:p] + M[:m]) 

print(main())