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)

mod=10**9+7
n,k=map(int,input().split())
arr=list(map(int,input().split()))
arr=sorted(arr,reverse=True,key=lambda x:abs(x))
if k==n:
  ans=1
  for i in range(n):
    ans*=arr[i]
    ans%=mod
  print(ans)
else:
  if k%2==1 and max(arr)<0:
    ans=1
    for i in range(k):
      ans*=arr[n-1-i]
      ans%=mod
    print(ans)
  else:
    ans=1
    cnt=0
    for i in range(k):
      if arr[i]<0:
        cnt+=1
      ans*=arr[i]
      ans%=mod
    if cnt%2==0:
      print(ans)
    else:
      min_plus=0
      min_minus=0
      for i in range(k):
        if arr[i]>=0:
          min_plus=arr[i]
        else:
          min_minus=arr[i]
      max_plus=0
      max_minus=0
      for i in range(k,n):
        if arr[i]>=0 and max_plus==0:
          max_plus=arr[i]
        if arr[i]<0 and max_minus==0:
          max_minus=arr[i]
      print(min_plus,min_minus,max_plus,max_minus)
      if min_plus*max_plus>=min_minus*max_minus:
        arr.remove(min_minus)
        ans=1
        for i in range(k-1):
          ans*=arr[i]
          ans%=mod
        ans*=max_plus
        ans%=mod
      else:
        arr.remove(min_plus)
        ans=1
        for i in range(k-1):
          ans*=arr[i]
          ans%-mod
        ans*=max_minus
        ans%=mod
      print(ans)