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)

N, K = gets.split.map(&:to_i)
A = gets.split.map(&:to_i)
MOD = 10 ** 9 + 7

zeros = A.select(&:zero?)
minus = A.select { |a| a < 0 }.sort
plus = A.select { |a| a > 0 }.sort
zcnt = zeros.size
mcnt = minus.size
pcnt = plus.size

def select_max(zeros, minus, plus)
  zcnt = zeros.size
  mcnt = minus.size
  pcnt = plus.size
  k = K
  val = 1

  while k > 0
    if mcnt >= 2 && pcnt >= 2 && k >= 2
      pv = plus[-2] * plus[-1]
      mv = minus[0] * minus[1]

      if pv < mv
        val *= mv

        minus.shift(2)
        mcnt -= 2
      else
        val *= pv

        plus.pop(2)
        pcnt -= 2
      end

      k -= 2
    elsif mcnt >= 2 && k >= 2
      a, b = minus.shift(2)

      val *= (a * b)

      mcnt -= 2
      k -= 2
    elsif pcnt >= 2 && k >= 2
      a, b = plus.pop(2)

      val *= (a * b)

      pcnt -= 2
      k -= 2
    elsif pcnt >= 1
      val *= plus.pop

      pcnt -= 1
      k -= 1
    elsif mcnt >= 1
      return -1
    else
      return 0
    end

    val %= MOD
  end

  val
end

def select_min(zeros, minus, plus)
  zcnt = zeros.size
  mcnt = minus.size
  pcnt = plus.size
  k = K
  val = 1

  while k > 0
    if mcnt >= 2 && pcnt >= 2 && k >= 2
      pv = plus[0] * plus[1]
      mv = minus[-2] * minus[-1]

      if pv > mv
        val *= mv

        minus.pop(2)
        mcnt -= 2
      else
        val *= pv

        plus.shift(2)
        pcnt -= 2
      end

      k -= 2
    elsif mcnt >= 2 && k >= 2
      a, b = minus.pop(2)

      val *= (a * b)

      mcnt -= 2
      k -= 2
    elsif pcnt >= 2 && k >= 2
      a, b = plus.shift(2)

      val *= (a * b)

      pcnt -= 2
      k -= 2
    elsif pcnt >= 1
      val *= plus.shift

      pcnt -= 1
      k -= 1
    elsif mcnt >= 1
      val *= minus.pop

      mcnt -= 1
      k -= 1
    else
      return 0
    end

    val %= MOD
  end

  val
end

values = []

if zcnt > 0
  values << 0
end

values << select_max(zeros.dup, minus.dup, plus.dup)
values << select_min(zeros.dup, minus.dup, plus.dup)

puts values.max