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)

import sys

from numpy.lib.function_base import kaiser
readline = sys.stdin.buffer.readline
read = sys.stdin.buffer.read

import numpy as np
import math


N, K = map(int, readline().rstrip().split())
AB = np.array(readline().rstrip().split(), np.int32)
p = 10 ** 9 + 7

A = AB[AB >= 0]
B = AB[AB < 0]

ans = 1
f = 1
if K == N:
    for a in A.tolist():
        ans *= a
        ans %= p
    for b in B.tolist():
        ans *= b
        ans %= p
else:
    A = np.sort(A)
    B = np.sort(B)
    if A.size == 0:
        if K % 2 == 0:
            for i in range(K):
                ans *= B[i]
                ans %= p
        else:
            for i in range(K):
                ans *= B[-i - 1]
                ans %= p

    else:
        AB = np.concatenate([A, B])
        AB = np.array(list(sorted(AB, key=lambda x: abs(x))))
        maxAB = max(AB)
        minAB = min(AB)
        AB = AB[-K:]
        for n in AB.tolist():
            ans *= n
            ans %= p
        
        if ans < 0:
            ans = ans / maxAB * minAB
            ans %= p


print(ans)