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)

import time
s = time.time()
import random as rnd
MOD = 1000000007

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

A.sort(key=abs)
A.reverse()

ans = A[0]
fact = 0

for i in range(1, K):
    ans = (ans * A[i])

indexes = [x for x in range(K)]

t = 0
while t <= 1.900:
    index1 = rnd.choice(indexes)
    while True:
        index2 = rnd.randint(0, N-1)
        if not (index2 in indexes):
            break


    old = ans
    
    ans //= A[index1]
    ans *= A[index2]

    if old >= ans:
        ans = old
    else:
        indexes.remove(index1)
        indexes.append(index2)
    t = time.time() - s

print(ans % 1000000007)