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)

n,k = list(map(int,input().split()))
A = list(map(int,input().split()))
mod = 10**9 + 7

if n == 1:exit(print(A[0]%mod))
A.sort()
if k == 1:exit(print(A[-1]%mod))
ans = 1

if A[-1] <= 0:
  for a in A[-k:]:
    ans = ans * a % mod
  exit(print(ans))
elif A[0] > 0:
  for a in A[-k:]:
    ans = ans * a % mod
  exit(print(ans))
else:
  i = 1
  while A[i] < 0:
    x, y = A[i-1], A[i]
    if x*y > A[-k+1]*A[-k]:
      ans = ans * x*y % mod
      k -= 2
      if k < 2:break
    i += 2
    if i > n:break
    else:
      break
  if k == 0: exit(print(ans))
  for a in A[-k:]:
    ans = ans * a % mod
  exit(print(ans))