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)

MOD=10**9+7
import sys
N,K=map(int,input().split())
alist=list(map(int,input().split()))

num_neg=0
num_pos=0
num_zero=0
aalist=[]
for a in alist:
  if a>0:
    num_pos+=1
  elif a<0:
    num_neg+=1
  else:
    num_zero+=1
  aalist.append((abs(a),a))
aalist.sort(reverse=True)
    
if num_zero>N-K:
  print(0)
  sys.exit(0)
  
if N==K:
  answer=1
  for a in alist:
    answer*=a
    answer%=MOD
  print(answer)
  sys.exit(0)
  
pos_possible=True
if num_pos==0:
  if K%2==1:
    pos_possible=False
    
if not pos_possible:
  aalist.sort()
  answer=1
  for i in range(K):
    aa,a=aalist[i]
    answer*=a
    answer%=MOD
  print(answer)
  sys.exit(0)
    
aalist.sort(reverse=True)
#print(aalist)
answer=1
sgn=1
for i in range(K-2):
  aa,a=aalist[i]
  answer*=a
  answer%=MOD
  if a<0:
    sgn*=-1

if sgn>0:
  if aalist[K-2][1]*aalist[K-1][1]>0:
    answer*=aalist[K-2][1]*aalist[K-1][1]
    answer%=MOD
  else:
    if aalist[K-2][1]*aalist[K][1]>0:
      answer*=aalist[K-2][1]*aalist[K][1]
      answer%=MOD
    else:
      answer*=aalist[K-1][1]*aalist[K][1]
      answer%=MOD
else:
  if aalist[K-2][1]*aalist[K-1][1]<0:
    answer*=aalist[K-2][1]*aalist[K-1][1]
    answer%=MOD
  else:
    if aalist[K-2][1]*aalist[K][1]<0:
      answer*=aalist[K-2][1]*aalist[K][1]
      answer%=MOD
    else:
      answer*=aalist[K-1][1]*aalist[K][1]
      answer%=MOD
    
print(answer)