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
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:
    if k % 2 == 1:
        if nz > 0:
            ans = 0
        else:
            am.sort()
            ans = -1 + MOD
            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:
        idx1 = np - 1
        idx2 = k - np + 1
        if k - np + 1 > nm:
            if nz > 0:
                ans = 0
            else:
                if nm % 2 == 1:
                    ans = -1 + MOD
                else:
                    ans = 1
                for i in range(np):
                    ans *= ap[i]
                    ans %= MOD
                for i in range(nm):
                    ans *= am[i]
                    ans %= MOD
        else:
            print(idx1, idx2)
            while idx1 >= 2 and idx2 + 1 < nm and \
                ap[idx1 - 1] * ap[idx1 - 2] < am[idx2] * am[idx2 + 1]:
                idx1 -= 2
                idx2 += 2
            print(idx1, idx2)
            ans = 1
            for i in range(idx1):
                ans *= ap[i]
                ans %= MOD
            for i in range(idx2):
                ans *= am[i]
                ans %= MOD
    else:
        idx1 = np
        idx2 = k - np
        while idx1 >= 2 and idx2 + 1 < nm and \
            ap[idx1 - 1] * ap[idx1 - 2] < am[idx2] * am[idx2 + 1]:
            idx1 -= 2
            idx2 += 2
        ans = 1
        for i in range(idx1):
            ans *= ap[i]
            ans %= MOD
        for i in range(idx2):
            ans *= am[i]
            ans %= MOD
else:
    idx1 = k
    idx2 = 0
    while idx1 >= 2 and idx2 + 1 < nm and \
        ap[idx1 - 1] * ap[idx1 - 2] < am[idx2] * am[idx2 + 1]:
        idx1 -= 2
        idx2 += 2
    ans = 1
    for i in range(idx1):
        ans *= ap[i]
        ans %= MOD
    for i in range(idx2):
        ans *= am[i]
        ans %= MOD

print(ans)