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: Accepted)

n,k = map(int,input().split())
a = list(map(int,input().split()))
s = []
f = []
z = 0
for ai in a:
  if ai > 0:
    s.append(ai)
  elif ai < 0:
    f.append(-ai)
  else:
    z += 1
p = len(s)
q = len(f)
l = max(0,k-p)
h = min(k,q)
mod = 10**9+7
if l > h:
  print(0)
  exit()
if l%2 == 0 or h-l >= 1:
  if l%2 == 0:
    c = l
  else:
    c = l+1
  s.sort(reverse=True)
  f.sort(reverse=True)
  while c+2 <= h:
    if f[c]*f[c+1] > s[k-c-1]*s[k-c-2]:
      c += 2
    else:
      break
  ans = 1
  for i in range(c):
    ans =(ans*f[i])%mod
  for i in range(k-c):
    ans = (ans*s[i])%mod
  print(ans)
  exit()
if z > 0:
  print(0)
  exit()
m = s + f
m.sort()
ans = 1
for i in range(k):
  ans = (ans*(m[i]))%mod
ans = (-ans)%mod
print(ans)