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: Accepted)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun May  3 16:22:00 2020

@author: neb0123
"""

def maxProductSubarrayOfSizeK(A, n, k): 
    A.sort() 
    product = 1
  
    if (A[n - 1] == 0 and (k & 1)): 
        return 0
  
    if (A[n - 1] <= 0 and (k & 1)) : 
        for i in range(n - 1, n - k - 1, -1): 
            product *= A[i] 
            product %= (10**9 + 7)
        return product 

    i = 0
    j = n - 1

    if (k & 1): 
        product *= A[j] 
        product %= (10**9 + 7)
        j-= 1
        k-=1
    k >>= 1

    for itr in range( k) : 
        left_product = A[i] * A[i + 1] 
        right_product = A[j] * A[j - 1] 
  
        if (left_product > right_product) : 
            product *= left_product 
            product %= (10**9 + 7)
            i += 2
          
        else : 
            product *= right_product
            product %= (10**9 + 7) 
            j -= 2

    return product

if __name__ == "__main__":
    N,K = map(int, input().split(' '))
    A = list(map(int,input().split(' ')))
    print(maxProductSubarrayOfSizeK(A,N,K))