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: Runtime Error)

import functools
import operator

prod = functools.partial(functools.reduce, operator.mul)


def main():
    n, k = map(int, input())
    a = map(int, input())

    a.sort(reversed=True)
    if a[-1] >= 0:
        print(prod(a[:k]))
        return
    if a[0] == 0:
        for i, _a in enumerate(a):
            if a[i] != 0:
                break
        else:
            print(0)
            return
        if k > len(a) - ind - 1:
            print(0)
            return
        if k % 2 == 1:
            print(0)
            return
        print(prod(a[len(a)-k:])
        return
    
    left = 0
    right = len(a) - 1
    ret = 1
    i = 0
    while i < k:
        if i < k - 1:
            if a[left] * a[left+1] < a[right] * a[right-1]:
                ret *= a[right] * a[right-1]
                right -= 2
            else:
                ret *= a[left] * a[left+1]
                left += 2
            i += 2
        else:
            ret *= a[left]
            left += 1
            i += 1
    print(ret)


if __name__ == "__main__":
    main()