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)

from collections import deque
import sys

N, K = map(int, input().split())
A = deque(sorted(list(map(int, input().split()))))

mod = 10 ** 9 + 7
num = 0
Ans = 1

while num < K-1:
    non_minus = A[-1] * A[-2]
    minus = A[0] * A[1]
    if non_minus > minus:
        Ans = Ans * A.pop() % mod
        num += 1
    else:
        Ans = Ans * A.popleft() * A.popleft() % mod
        num += 2

if num == K - 1:
    Ans = Ans * A[-1] % mod
    
if A[-1] < 0 and K % 2 == 1:
    Ans = 1
    for i in range(K):
        Ans = Ans * A[i] % mod

print(Ans)