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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

from collections import deque

mod = 1000000007

n,k = map(int,input().split())

a = list(map(int,input().split()))

plus_1 = deque()
minus_1 = deque()
plus_2 = deque()
minus_2 = deque()

a.sort()

for i in a:
    if i > 0:
        plus_2.append(i)
    else:
        minus_1.append(i)

a.sort(reverse=True)

for i in a:
    if i > 0:
        plus_1.append(i)
    else:
        minus_2.append(i)

maxa = 1

mini = 1

i = 0

while i < k:
    if len(plus_1) > 1 and len(minus_1) > 1:
        if plus_1[0]*plus_1[1] < minus_1[0]*minus_1[1] and i+2<=k:
            maxa *= minus_1[0]*minus_1[1]
            minus_1.popleft()
            minus_1.popleft()
            i += 2
        else:
            maxa *= plus_1[0]
            plus_1.popleft()
            i += 1
    elif len(plus_1):
        maxa *= plus_1[0]
        plus_1.popleft()
        i += 1
    else:
        maxa *= minus_1[0]
        minus_1.popleft()
        i += 1

i = 0

while i < k:
    if len(plus_2) and len(minus_2):
        if plus_2[0] < abs(minus_2[0]):
            mini *= plus_2[0]
            plus_2.popleft()
        else:
            mini *= minus_2[0]
            minus_2.popleft()
    elif len(plus_2):
        mini *= plus_2[0]
        plus_2.popleft()
    else:
        mini *= minus_2[0]
        minus_2.popleft()
    i += 1

if maxa > 0:
    print(maxa%mod)
else:
    print(mini%mod)