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 Ruby (2.7.1) (judge verdict: Wrong Answer)

DIV = 10 ** 9 + 7

N, K = $stdin.gets.split.map {|i| i.to_i }
Ap = []
$total = 0
$zero = 0
$plus = 0
$minus = 0
$stdin.gets.split.each {|i|
  $total += 1
  v = i.to_i
  if v == 0
    $zero += 1
  elsif v > 0
    Ap.push([v, false])
    $plus += 1
  else # v < 0
    Ap.push([-v, true])
    $minus += 1
  end
}
Am = Ap.dup
Ap.sort! {|x, y| y[0] <=> x[0] }
Am.sort! {|x, y| x[0] <=> y[0] }

result = nil
if $zero > $total - K
  result = 0
elsif $plus >= 1
  k = 0
  result = 1
  prev_minus = nil
  Ap.each do |a|
    if a[1] # minus
      if prev_minus
        if K - k >= 2
          result = (result * prev_minus * a[0]) % DIV
          prev_minus = nil
          k += 2
        end
      else # prev_minus is nil
        prev_minus = a[0]
      end
    else # plus
      result = (result * a[0]) % DIV
      k += 1
    end
    break if k == K
  end
  if k != K
    result = 0
  end
else
  k = 0
  result = 1
  Am.each do |a|
    result = (result * a[0] + DIV) % DIV
  end
end
puts result