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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

import sys

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    import bisect

    n, k = map(int, readline().split())
    a = list(map(int, readline().split()))
    a.sort()

    neg = bisect.bisect_left(a, 0)
    zer = bisect.bisect_right(a, 0) - neg
    pos = n - (neg + zer)

    a_neg = a[:neg]
    a_pos = a[-pos:] if pos > 0 else []
    a_pos.sort(reverse=True)

    ans = 0
    flag = False

    if k % 2 == 0:
        a2 = []
        for i in range(0, pos - 1, 2):
            a2.append(a_pos[i] * a_pos[i + 1])
        for i in range(0, neg - 1, 2):
            a2.append(a_neg[i] * a_neg[i + 1])
        a2.sort(reverse=True)
        if len(a2) * 2 >= k:
            flag = True
            ans = 1
            for i in range(k // 2):
                ans *= a2[i]
                ans %= MOD
    else:
        a2 = []
        for i in range(1, pos - 1, 2):
            a2.append(a_pos[i] * a_pos[i + 1])
        for i in range(0, neg - 1, 2):
            a2.append(a_neg[i] * a_neg[i + 1])
        a2.sort(reverse=True)
        if pos > 0 and len(a2) * 2 + 1 >= k:
            flag = True
            ans = a_pos[0]
            for i in range(k // 2):
                ans *= a2[i]
                ans %= MOD

    if not flag:
        if zer > 0:
            ans = 0
        elif k % 2 == 0:
            b2 = []
            a_pos.sort()
            a_neg.sort(reverse=True)

            for i in range(1, neg - 1, 2):
                b2.append(a_neg[i] * a_neg[i + 1])
            for i in range(1, pos - 1, 2):
                b2.append(a_pos[i] * a_pos[i + 1])
            b2.sort()
            if len(b2) * 2 + 2 >= k:
                ans = a_pos[0] * a_neg[0]
                for i in range(k // 2):
                    ans *= b2[i]
                    ans %= MOD
        else:
            b2 = []
            a_pos.sort()
            a_neg.sort(reverse=True)
            for i in range(1, neg - 1, 2):
                b2.append(a_neg[i] * a_neg[i + 1])
            for i in range(0, pos - 1, 2):
                b2.append(a_pos[i] * a_pos[i + 1])
            b2.sort()
            if neg > 0 and len(b2) * 2 + 1 >= k:
                ans = a_neg[0]
                for i in range(k // 2):
                    ans *= b2[i]
                    ans %= MOD

    print(ans)

if __name__ == '__main__':
    main()