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)


def main():
    n,k=map(int,input().split())
    A = map(int,input().split())

    def prod(iterables):
        res = None
        for element in iterables:
            tmp = 1
            for e in element:
                tmp *= e
            if res is None or tmp > res:
                res = tmp
        return res
    
    pos, neg = [], []
    for a in A:
        if a >= 0:
            pos.append(a)
        else:
            neg.append(a)

    pos_n, neg_n = len(pos), len(neg)
    ans = None

    for i in range(neg_n):
        if k-i > pos_n:
            continue
        tmp = prod(permutations(neg, i)) * prod(permutations(pos, k-i)) % (10**9+7)
        if ans is None or tmp > ans:
            ans = tmp
    print(ans)
main()