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)

MOD = 10**9 + 7
n, k = map(int, input().split())
a = list(map(int, input().split()))
am = []
ap = []
for ai in a:
    if ai > 0:
        ap.append(ai)
    elif ai < 0:
        am.append(-ai)
am.sort(reverse=True)
ap.sort(reverse=True)

nm = len(am)
np = len(ap)
nz = n - np - nm
# print(am)
# print(ap)

if np + nm < k:
    ans = 0
elif np == 0:
    pass
    if k % 2 == 1:
        am.sort()
        ans = -1
        for i in range(k):
            ans *= am[i]
            ans %= MOD
    else:
        ans = 1
        for i in range(k):
            ans *= am[i]
            ans %= MOD
elif np < k:
    if (k - np) % 2 == 1:
        x = np - 1
        idx = k - np + 1
    else:
        x = np
        idx = k - np

    while idx + 2 <= x and idx + 1 < nm and ap[x - idx - 1] * ap[
            x - idx - 2] < am[idx] * am[idx + 1]:
        idx += 2
    ans = 1
    for i in range(x - idx):
        ans *= ap[i]
        ans %= MOD
    for i in range(idx):
        ans *= am[i]
        ans %= MOD
else:
    idx = 0
    while idx + 2 <= k and idx + 1 < nm and ap[k - idx - 1] * ap[
            k - idx - 2] < am[idx] * am[idx + 1]:
        idx += 2
    ans = 1
    for i in range(np - idx):
        ans *= ap[i]
        ans %= MOD
    for i in range(idx):
        ans *= am[i]
        ans %= MOD

print(ans)