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: Time Limit Exceeded)

class Node
  attr_reader :value, :left, :right

  def initialize(value, left = nil, right = nil)
    @value = value
    @left = left
    @right = right
  end

  def insert(elt)
    d = elt <=> @value

    if d < 0
      Node.new(@value,
               left ? left.insert(elt) : Node.new(elt),
               right)
    elsif d > 0
      Node.new(@value,
               left,
               right ? right.insert(elt) : Node.new(elt))
    else # d == 0
      self
    end
  end

  def min_value
    if @left.nil?
      @value
    else
      @left.min_value
    end
  end

  def remove(elt)
    d = elt <=> @value

    if d < 0
      Node.new(@value,
               @left ? @left.remove(elt) : Node.new(elt),
               @right)
    elsif d > 0
      Node.new(@value,
               @left,
               @right ? @right.remove(elt) : Node.new(elt))
    else # d == 0
      if @left.nil? && @right.nil?
        nil
      elsif @left.nil?
        @right
      elsif @right.nil?
        @left
      else # @right && @left
        min = @right.min_value
        Node.new(min,
                 @left,
                 @right.remove(min))
      end
    end
  end
end

class Set
  def initialize
    @tree = nil
  end

  def min
    @tree&.min_value
  end

  def insert(elt)
    if @tree.nil?
      @tree = Node.new(elt)
    else
      @tree = @tree.insert(elt)
    end
  end

  def remove(elt)
    unless @tree.nil?
      @tree = @tree.remove(elt)
    end
  end
end

n, q = gets.split.map(&:to_i)

constructions = n.times.map { gets.split.map(&:to_i) }
start_times = q.times.map { gets.to_i }
events = constructions.flat_map { |s, t, x|
  [[s - x, :push, x],
   [t - x, :delete, x]]
}.sort
set = Set.new

i = 0
start_times.each do |d|

  while i < events.size
    t, meth, x = events[i]

    if t <= d
      case meth
      when :push
        set.insert(x)
      when :delete
        set.remove(x)
      end
    else
      break
    end
    i += 1
  end

  puts set.min || -1
end