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)

n, k = map(int, input().split())
a_list = sorted(map(int, input().split()),reverse=True)

l_minus = sorted([i for i in a_list if i < 0])
l_plus =  sorted([i for i in a_list if i > 0],reverse=True)
l_zero = [i for i in a_list if i == 0]

# マイナスは2個セットで選びたい
# 最大化問題か最小か問題かを知りたい
# マイナスを奇数個選ばないといけないのが辛い時
_min = False
if (k - len(l_plus)) % 2 == 1:
  _min = True
  # 最悪
cnt = 0
ans = 1
if _min == False:
  while 1:
    if cnt == k:
      break
    if k - cnt >= 2 and len(l_minus) >= 2 and len(l_plus) >= 2:
      a = l_minus[0] * l_minus[1]
      b = l_plus[0] * l_plus[1]
      if a >= b:
        l_minus.pop(0)
        l_minus.pop(0)
        ans *= a
      else:
        l_plus.pop(0)
        l_plus.pop(0)
        ans *= b
      cnt += 2
    else:
      cnt += 1
      ans *= l_plus.pop(0)
else:
  if len(l_zero) > 0:
    ans = 0
  else:
    l_minus = sorted(l_minus, reverse=True)
    l_plus =  sorted(l_plus)
    while 1:
      if cnt == k:
        break
      if k - cnt >= 2 and len(l_minus) >= 2 and len(l_plus) >= 2:
        a = l_minus[0] * l_minus[1]
        b = l_plus[0] * l_plus[1]
        if a >= b:
          l_minus.pop(0)
          l_minus.pop(0)
          ans *= a
        else:
          l_plus.pop(0)
          l_plus.pop(0)
          ans *= b
        cnt += 2
      else:
        cnt += 1
        ans *= l_minus.pop(0)
        
print(ans % (pow(10,9) + 7))