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)

N,K = map(int, input().split())
A = list(map(int, input().split()))
APlus = []
AMinus = []
for i in A:
    if 0 < i:
        APlus.append(i)
    elif 0 == i:
        pass
    elif i < 0:
        AMinus.append(i)
APlusBackup = APlus = sorted(APlus)
AMinusBackup = AMinus = sorted(AMinus)
count = 0
answer = 1
while count < K:
    if count + 1 < K and 1 < len(APlus) and 1 < len(AMinus):
        if AMinus[0] * AMinus[1] < APlus[0] * APlus[1]:
            answer = answer * APlus.pop(0)
            answer = answer * APlus.pop(0)
            count += 2
        elif APlus[0] * APlus[1] < AMinus[0] * AMinus[1]:
            answer = answer * AMinus.pop(0)
            answer = answer * AMinus.pop(0)
            count += 2
        elif AMinus[0] * AMinus[1] == APlus[0] * APlus[1]:
            if count + 2 < K:
                if AMinus[2] <= APlus[2]:
                    answer = answer * APlus.pop(0)
                    answer = answer * APlus.pop(0)
                    count += 2
                else:
                    answer = answer * AMinus.pop(0)
                    answer = answer * AMinus.pop(0)
                    count += 2
    else:
        try:
            answer = answer * APlus.pop(0)
            count += 1
        except:
            count = 0
            answer = 1
            APlus = sorted(APlusBackup, reverse = True)
            AMinus = sorted(AMinusBackup, reverse = True)
            while count < K:
                try:
                    if APlus[0] < AMinus[0]:
                        answer = answer * APlus.pop(0)
                        count += 1
                    elif AMinus[0] < APlus[0]:
                        answer = answer * AMinus.pop(0)
                        count += 1
                    elif APlus[0] == AMinus[0]:
                        if 1 < len(APlus) and 1 < len(AMinus):
                            if APlus[1] <= AMinus[1]:
                                answer = answer * APlus.pop(0)
                                count += 1
                            else:
                                answer = answer * AMinus.pop(0)
                                count += 1
                        else:
                            answer = answer * APlus.pop(0)
                            count += 1
                except:
                    answer = answer * AMinus.pop(0)
                    count += 1
answer = answer % (10 ** 9 + 7)
print(answer)