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: Runtime Error)

import bisect
N,K=map(int,input().split())
A=list(map(int,input().split()))
Plis=[]
Nlis=[]
for i in range(N):
  if A[i] >=0:
    bisect.insort(Plis,A[i])
  else:
    bisect.insort(Nlis,A[i])
Plis.reverse()

pn=len(Plis)
nn=N-pn

Ppro=[1]
Npro=[1]

for i in range(pn):
  Ppro+=[Ppro[i]*Plis[i]]
  
for j in range(nn):
  Npro+=[Npro[j]*Nlis[j]]


if N==K:
  print(Npro[-1]*Ppro[-1]%(10**9+7))
elif pn==0 and K%2==1:
  ans=int(Npro[-1]/Npro[-1-K])%(10**9+7)
  print(ans)
else:
  ans=0
  maxn = min(K,nn)
  maxn = (maxn//2)*2  
  for i in range(maxn//2):
    if Npro[2*i]*Ppro[K-2*i] >ans:
      ans =Npro[2*i]*Ppro[K-2*i]
  ans = ans%(10**9+7)
  print(ans)