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():
    from collections import deque
    import bisect
    n, k = map(int, readline().split())
    a = list(map(int, readline().split()))
    a.sort()
    que = deque()

    if n == k:
        que.extend(a)
    elif a[-1] < 0 and k % 2 == 1:
        que.extend(a)
        for _ in range(n - k):
            que.popleft()
    else:
        b = [[] for _ in range(n)]
        for i in range(n):
            b[i] = [abs(a[i]), a[i] // abs(a[i])]
        b.sort(reverse=True)
        b = deque(b)
        que1 = deque()
        que2 = deque()
        sign = 1

        for i in range(k):
            val, sg = b.popleft()
            if sg >= 0:
                que1.append(val)
            else:
                que2.append(val)
                sign *= -1

        if sign == -1:
            add1, add2 = 0, 0
            rmv1, rmv2 = 10 ** 19, 10 ** 19
            if que1:
                rmv1 = que1[-1]
                for x, sign in b:
                    if sign == -1:
                        add1 = x
                        break
            if que2:
                rmv2 = que2[-1]
                for x, sign in b:
                    if sign == 1:
                        add2 = x
                        break

            if add1 * rmv2 > add2 * rmv1:
                que2.append(add1)
                que1.pop()
            else:
                que1.append(add2)
                que2.pop()

        que.extend(que1)
        que.extend(que2)

    while len(que) > 1:
        que.append(que.popleft() * que.popleft())

    print(que.popleft() % MOD)


if __name__ == '__main__':
    main()