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: Wrong Answer)

from heapq import heappush,heappop,heapify
MOD = 10**9+7

n,k = map(int,input().split())
a = list(map(int,input().split()))

hqp = []
hqm = []
for ai in a:
  if ai >= 0:
    heappush(hqp,-ai)
  else:
    heappush(hqm,ai)

ans = 1
if k-len(hqp) > 0 and (k-len(hqp))%2 == 1:
  hqp = []
  hqm = []
  for ai in a:
    if ai >= 0:
      heappush(hqp,ai)
    else:
      heappush(hqm,-ai)
  while(k > 0):
    if k > 1:
      if len(hqp) > 1 and len(hqm) > 1:
        if hqp[0]*hqp[1] > hqm[0]*hqm[1]:
          ans *= hqp[0]*hqp[1]
          heappop(hqp)
          heappop(hqp)
        else:
          ans *= hqm[0]*hqm[1]
          heappop(hqm)
          heappop(hqm)
      elif len(hqp) <= 1 and len(hqm) > 1:
        ans *= hqm[0]*hqm[1]
        heappop(hqm)
        heappop(hqm)
      elif len(hqp) > 1 and len(hqm) <= 1:
        ans *= hqp[0]*hqp[1]
        heappop(hqp)
        heappop(hqp)
      else:
        ans *= hqp[0]*-hqm[0]
        heappop(hqp)
        heappop(hqm)
      k -= 2
    else:
      if len(hqp) > 0:
        ans *= hqp[0]
        heappop(hqp)
      else:
        ans *= -hqm[0]
        heappop(hqm)
      k -= 1
    ans %= MOD
else:
  while(k > 0):
    if k > 1:
      if len(hqp) > 1 and len(hqm) > 1:
        if hqp[0]*hqp[1] > hqm[0]*hqm[1]:
          ans *= hqp[0]*hqp[1]
          heappop(hqp)
          heappop(hqp)
        else:
          ans *= hqm[0]*hqm[1]
          heappop(hqm)
          heappop(hqm)
      elif len(hqp) <= 1 and len(hqm) > 1:
        ans *= hqm[0]*hqm[1]
        heappop(hqm)
        heappop(hqm)
      elif len(hqp) > 1 and len(hqm) <= 1:
        ans *= hqp[0]*hqp[1]
        heappop(hqp)
        heappop(hqp)
      else:
        ans *= -hqp[0]*hqm[0]
        heappop(hqp)
        heappop(hqm)
      k -= 2
    else:
      if len(hqp) > 0:
        ans *= -hqp[0]
        heappop(hqp)
      else:
        ans *= hqm[0]
        heappop(hqm)
      k -= 1
    ans %= MOD
print(ans)