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)

#!/usr/bin/env python3
from functools import reduce

mod = 10**9 + 7
n, k, *a = map(int, open(0).read().split())
a.sort(key=lambda x: abs(x))
ans = reduce(lambda a, b: (a * b) % mod, a[-k:])

c = a[-k:]
j = sum(i < 0 for i in c) % 2
if j:
    c = a[-k:]
    neg = [i for i in c if i < 0]
    pos = [i for i in c if i > 0]
    b = sorted(a[:n - k])
    if b == []:
        print(ans)
        exit()
    if neg == []:
        if pos[0] * b[0] < 0:
            ans = ans * pow(pos[0], mod - 2, mod) * b[0] % mod
        else:
            ans = reduce(lambda a, b: (a * b) % mod, a[:k])
    elif pos == []:
        if neg[0] * b[-1] < 0:
            ans = ans * pow(neg[0], mod - 2, mod) * b[-1] % mod
        else:
            ans = reduce(lambda a, b: (a * b) % mod, a[:k])
    elif pos[0] * b[-1] > neg[0] * b[0] and pos[0] * b[0] < 0:
        ans = ans * pow(pos[0], mod - 2, mod) * b[0] % mod
    elif 0 > b[-1] * neg[0]:
        ans = ans * pow(neg[0], mod - 2, mod) * b[-1] % mod
    else:
        ans = reduce(lambda a, b: (a * b) % mod, a[:k])
print(ans)