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: Wrong Answer)

def main():

    N, K = map(int, input().split())
    A = sorted([int(i) for i in input().split()])
    MOD = 10 ** 9 + 7
    ans = 0

    start = 0
    end = N - 1
    k, m = divmod(K, 2)
    for i in range(k):
        start_sum = A[start] * A[start + 1]
        end_sum = A[end] * A[end - 1]
        # print(start_sum, end_sum, k)
        if start_sum >= end_sum:
            ans += start_sum % MOD
            ans %= MOD
            start += 2
        else:
            ans += end_sum % MOD
            ans %= MOD
            end -= 2

    if m:
        ans += A[start]

    print(ans)


if __name__ == '__main__':
    main()