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: Runtime Error)

import numpy as np

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

A = sorted(A)
A = np.array(A)
A = A % (10**9+7)

dp = [0 for i in range(N//4+1)]

for i in range(N//4+1):
  if i == 0:
    a = A[-K:]
    prod = 1
    for j in range(len(a)):
      prod *= a[i]
      prod = prod % (10**9+7)
    dp[0] = prod
  else:
    if -K+i*2 < 0:
      a = np.hstack([A[:i*2], A[-K+i*2:]])
      prod = 1
      for j in range(len(a)):
        prod *= a[i]
        prod = prod % (10**9+7)
      dp[i] = prod
    else:
      a = A[:i*2]
      prod = 1
      for j in range(len(a)):
        prod *= a[i]
        prod = prod % (10**9+7)
      dp[i] = prod

print(max(dp))