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 sys, bisect


if(__name__ == "__main__"):

    N, K = map( int, input().strip().split() )
    divisor = 10**9+7

    list_a = list( map(int, input().strip().split()) )

    """
    left, right側の2項の積で大きい方を選択
    選べるのが残り1項ならright側を選択
    """
    multiplies = 1

    if(N==K):
        for i in range(N):
            multiplies = multiplies * list_a[i] % divisor
        print(multiplies)
    else:
        list_a.sort()

        flag_overzero = True
        if(list_a[-1] < 0 and K % 2 != 0):
            flag_overzero = False
        """
        解が負になるのはN>Kの時には
        正の項が1つもなく、Kが奇数の時
        """
        if(flag_overzero == True):
            left = 0
            right = N-1
            multiply_left = list_a[left] * list_a[left+1]
            multiply_right = list_a[right] * list_a[right-1]
            flag_left = True

            while(K>0):
                if(K>1):
                    K -= 2

                    if(multiply_left < multiply_right):
                        multiply_right %= divisor
                        multiplies = multiplies * multiply_right % divisor
                        right -= 2
                        flag_left=False
                        multiply_right = list_a[right] * list_a[right-1]

                    else:
                        multiply_left %= divisor
                        multiplies = multiplies * multiply_left % divisor
                        left += 2
                        flag_left=True
                        multiply_left = list_a[left] * list_a[left+1]

                else:
                    multiplies = multiplies * list_a[right] % divisor
                    K =0
            print(multiplies)
        else:
            list_a = [ abs(list_a[i]) for i in range(N)]
            list_a.sort()
            for i in range(K):
                multiplies = multiplies * list_a[i] % divisor
            multiplies = -multiplies %divisor

            print(multiplies)