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: Wrong Answer)

import sys
input = sys.stdin.readline
#-------------
n,k = map(int,input().split())
a = list(map(int,input().split()))
#-------------
a.sort(reverse = True)
w = 10**9 + 7
ans = 1
if k%2 == 1:#kは奇数
  for i in range(k):
    ans *= a[i]
  print(ans % w)

else:#kは偶数
  if n%2 == 0:#nは偶数
    A = n//2
    a_new = [a[2*i]*a[2*i+1] for i in range(A)]
    a_new.sort(reverse = True)
    for j in range(k//2):
      ans *= a_new[j]
    print(ans % w)
      
  else:#nは奇数
    a_plus =[]
    a_minus = []
    pos = 0
    neg = 0
    for i in range(n):
      if a[i] > 0 :
        a_plus.append(a[i])
        pos += 1
      else :
        a_minus.append(a[i])
        neg += 1
    a_plus.sort(reverse = True)
    a_minus.sort()
    a_plus_new = [a_plus[2*i]*a_plus[2*i+1] for i in range(pos//2)]
    a_minus_new = [a_minus[2*i]*a_minus[2*i+1] for i in range(neg//2)]
    a_new = a_plus_new + a_minus_new
    a_new.sort(reverse = True)
    for j in range(k//2):
      ans *= a_new[j]
    print(ans % w)