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)

MOD = 10 ** 9 + 7


def mod_mul(arr, mod):
    res = 1
    for elem in arr:
        res *= elem
        res %= mod
    return res


def main():
    n, k = map(int, input().split())
    a = list(map(int, input().split()))
    a.sort(key=lambda x: abs(x), reverse=True)

    if all([e <= 0 for e in a]):
        if k % 2 == 0:
            print(mod_mul(a[:k], MOD))
        else:
            print(mod_mul(a[n - k:], MOD))
        return

    if k == 1:
        print(max(a))
        return

    if k == n:
        print(mod_mul(a, MOD))
        return

    res = 1
    if sum(a[i] < 0 for i in range(k)) % 2 == 1:
        minus_flag = False
        for i in range(k - 1, -1, -1):
            if a[i] < 0:
                if not minus_flag:
                    minus_flag = True
                else:
                    res *= a[i]
                    res %= MOD
            else:
                res *= a[i]
                res %= MOD
        for i in range(k, n):
            if a[i] >= 0:
                res *= a[i]
                res %= MOD
                break
    else:
        for i in range(k):
            res *= a[i]
            res %= MOD

    print(res)


main()