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 sys
p= 10**9+7
n,k=map(int,input().split())
a=list(map(int,input().split()))
right = list()
left = list()
zero = 0
for x in a:
  if x > 0:
    right.append(x)
  elif x < 0:
    left.append(x)
  else:
    zero += 1
if n - k < zero or (k%2 and len(right)==0 and zero>0):
  # 0を必ず取らないといけない場合、期待される最大が負のとき
  print(0)
  sys.exit()
right.sort(reverse=True)
if len(right)==0:
  #負の数だけ
  left.sort(reverse=k%2)
  left_r = k
  right_r = 0
elif len(left)==0:
  #正の数だけ
  left_r = 0
  right_r = k
else:
  #それ以外の場合はいったんrightからとりきって残りをleftから取る
  # 偶数個のときはrightを偶数に、奇数のときは奇数個にする
  left.sort()
  # len(right)とkの偶奇が一致-> rightを全部突っ込む(かk個突っ込む)
  right_r = min(k, len(right)) - (len(right)%2 ^ k%2)
  left_r = max(0, k - len(right)) + (len(right)%2 ^ k%2)
  while left_r < len(left) -1 or right_r > 1:
    if left[left_r]*left[left_r+1] > right[right_r-1]*right[right_r-2]:
      left_r += 2
      right_r -= 2
    else:
      break
ans = 1
for i in range(right_r):
  ans = (ans * right[i]) % p
for i in range(left_r):
  ans = (ans * left[i]) % p
print(ans)