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)

class PriorityQueue
  # min heap
  def initialize(source = [])
    @heap = []
    source.each { |e| push(e) }
  end

  def size
    @heap.size
  end

  def empty?
    @heap.empty?
  end

  def top
    @heap.first
  end

  def push(value)
    @heap << value
    new_node_index = @heap.size - 1

    while new_node_index > 0 do
      parent_node_index = (new_node_index - 1) / 2

      break if @heap[parent_node_index] <= value

      @heap[parent_node_index], @heap[new_node_index] = @heap[new_node_index], @heap[parent_node_index]
      new_node_index = parent_node_index
    end

    @heap[new_node_index] = value
  end

  def pop
    min = top

    tmp_node = @heap.pop

    tmp_index = 0
    while (tmp_index * 2 + 1) < size
      tmp_left_child_index  = tmp_index * 2 + 1
      tmp_right_child_index = tmp_index * 2 + 2
      min_child_index = tmp_left_child_index

      if tmp_right_child_index < size && @heap[tmp_left_child_index] > @heap[tmp_right_child_index]
        min_child_index = tmp_right_child_index
      end

      break if @heap[min_child_index] >= tmp_node

      @heap[tmp_index] = @heap[min_child_index]
      tmp_index = min_child_index
    end

    @heap[tmp_index] = tmp_node unless empty?

    min
  end
end

N,K = gets.split.map(&:to_i)
A = gets.split.map(&:to_i)

MOD = 10**9 + 7

plus_pq = PriorityQueue.new
minus_pq = PriorityQueue.new

A.each do |a_v|
  if a_v >= 0
    plus_pq.push(-1 * a_v)
  end
  if a_v < 0
    minus_pq.push(a_v)
  end
end

ans = 1

if plus_pq.size == 0 && K.odd? # 積が負になる時
  minus_pq = A.sort.reverse
  K.times do |i|
    ans *= minus_pq[i]
    ans %= MOD
  end

  puts ans
else  # 積が正になる時
  cnt = K

  while cnt > 0
    if cnt >= 2 && minus_pq.size >= 2 && plus_pq.size >= 2
      minus_1 = minus_pq.pop
      minus_2 = minus_pq.pop

      plus_1 = plus_pq.pop
      plus_2 = plus_pq.pop

      if minus_1 * minus_2 >= plus_1 * plus_2
        ans *= minus_1 * -1
        ans %= MOD
        ans *= minus_2 * -1
        ans %= MOD

        plus_pq.push(plus_1)
        plus_pq.push(plus_2)
      else
        ans *= plus_1 * -1
        ans %= MOD
        ans *= plus_2 * -1
        ans %= MOD

        plus_pq.push(minus_1)
        plus_pq.push(minus_2)
      end
      cnt -= 2
    elsif cnt >= 2 && minus_pq.size >= 2 && plus_pq.size == 1
      minus_1 = minus_pq.pop
      minus_2 = minus_pq.pop

      ans *= minus_1 * -1
      ans %= MOD
      ans *= minus_2 * -1
      ans %= MOD

      cnt -= 2
    elsif cnt == 1 && plus_pq.size >= 1
      plus_1 = plus_pq.pop
      ans *= plus_1 * -1
      ans %= MOD

      cnt -= 1
    elsif plus_pq.size == 0
      minus_1 = minus_pq.pop
      ans *= minus_1
      ans %= MOD
      cnt -= 1
    elsif minus_pq.size == 0
      plus_1 = plus_pq.pop
      ans *= plus_1 * -1
      ans %= MOD
      cnt -= 1
    else
      plus_1 = plus_pq.pop
      ans *= plus_1 * -1
      ans %= MOD
      cnt -= 1
    end
  end

  puts ans
end