Problem:
Score : 500 points

Problem Statement

There is an infinitely long street that runs west to east, which we consider as a number line.

There are N roadworks scheduled on this street.
The i-th roadwork blocks the point at coordinate X_i from time S_i - 0.5 to time T_i - 0.5.

Q people are standing at coordinate 0. The i-th person will start the coordinate 0 at time D_i, continue to walk with speed 1 in the positive direction and stop walking when reaching a blocked point.

Find the distance each of the Q people will walk.

Constraints

All values in input are integers.

1 \leq N, Q \leq 2 \times 10^5

0 \leq S_i < T_i \leq 10^9

1 \leq X_i \leq 10^9

0 \leq D_1 < D_2 < ... < D_Q \leq 10^9

If i \neq j and X_i = X_j, the intervals [S_i, T_i) and [S_j, T_j) do not overlap.

Input

Input is given from Standard Input in the following format:

N Q
S_1 T_1 X_1
:
S_N T_N X_N
D_1
:
D_Q

Output

Print Q lines. The i-th line should contain the distance the i-th person will walk or -1 if that person walks forever.

Sample Input 1

4 6
1 3 2
7 13 10
18 20 13
3 4 2
0
1
2
3
5
8

Sample Output 1

2
2
10
-1
13
-1

The first person starts coordinate 0 at time 0 and stops walking at coordinate 2 when reaching a point blocked by the first roadwork at time 2.

The second person starts coordinate 0 at time 1 and reaches coordinate 2 at time 3. The first roadwork has ended, but the fourth roadwork has begun, so this person also stops walking at coordinate 2.

The fourth and sixth persons encounter no roadworks while walking, so they walk forever. The output for these cases is -1.

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

class PriorityQueue
  attr_reader :size

  def initialize(order: :asc)
    @size = 0
    @nodes = []
  end

  def empty?
    @size.zero?
  end

  def push(node)
    index = size
    @size += 1

    while index > 0
      parent = (index - 1) / 2

      break if (@nodes[parent] <=> node) <= 0

      @nodes[index] = @nodes[parent]
      index = parent
    end

    @nodes[index] = node
  end

  alias_method :<<, :push

  def pop
    node = @nodes.first
    root = @nodes[size - 1]
    @size -= 1
    index = 0

    while index * 2 + 1 < @size
      left = 2 * index + 1
      right = left + 1

      if right < size && (@nodes[right] <=> @nodes[left]) <= 0
        left = right
      end

      break if (@nodes[left] <=> root) > 0

      @nodes[index] = @nodes[left]
      index = left
    end

    @nodes[index] = root
    node
  end

  def top
    @nodes.first
  end
end

N, Q = gets.split.map(&:to_i)
W = N.times.map { gets.split.map(&:to_i) }
D = Q.times.map { gets.to_i }

D << Float::INFINITY

start_work = Hash.new { |h, k| h[k] = [] }
finish_work = Hash.new { |h, k| h[k] = [] }

W.each_with_index do |(s, t, x), work_id|
  start = s - x
  finish = t - x - 1

  left = D.bsearch_index { |d| d >= start }
  right = D.bsearch_index { |d| d >= finish }

  if finish < D[right]
    right -= 1
  end

  start_work[left] << [x, work_id]
  finish_work[right + 1] << work_id
end

Node = Struct.new(:x, :work_id) do
  def <=>(node)
    x <=> node.x
  end
end

pque = PriorityQueue.new

ans = Array.new(N, Float::INFINITY)
finished = Hash.new(false)

Q.times do |i|
  start_work[i].each do |x, work_id|
    pque.push(Node.new(x, work_id))
  end

  finish_work[i].each do |work_id|
    finished[work_id] = true
  end

  while pque.size > 0 && finished[pque.top.work_id]
    pque.pop
  end

  if pque.empty?
    ans[i] = -1
  else
    ans[i] = pque.top.x
  end
end

puts ans