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: Time Limit Exceeded)

#!/usr/bin/env python

def main():
    n, k = map(int, input().split())
    a = list(map(int, input().split()))
    mod = 10**9+7

    a.sort()
    ret = 1
    if k % 2 == 0 or a[-1] >= 0:
        for _ in range(k//2):
            mlt1 = a[0] * a[1]
            mlt2 = a[-2] * a[-1]
            if mlt1 >= mlt2:
                ret *= mlt1 % mod
                a = a[2:]
            else:
                ret *= mlt2 % mod
                a = a[:-2]
            ret %= mod

        if k % 2 == 1:
            ret *= a[-1]
            ret %= mod

    else:
        for i in range(k):
            ret *= a[n-1-i]
            ret %= mod

    print(ret)


if __name__ == '__main__':
    main()