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_accessor :value, :left, :right

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

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

  def each
    @left&.each { |elt| yield(elt) }
    yield(@value)
    @right&.each { |elt| yield(elt) }
    self
  end

end

class Set
  attr_accessor :tree

  def initialize
    @tree = nil
  end

  def min
    @tree&.min_value
  end

  def insert(elt)
    node = @tree
    parent = self
    setter = :"tree="

    while true
      if node.nil?
        parent.send(setter, Node.new(elt))
        break
      end

      d = elt <=> node.value
      if d < 0
        parent = node
        setter = :"left="
        node = node.left
      elsif d > 0
        parent = node
        setter = :"right="
        node = node.right
      else
        break
      end
    end
  end

  def remove(elt)
    _remove(self, :"tree=", @tree, elt)
  end

  def _remove(parent, setter, node, elt)
    while node
      d = elt <=> node.value
      if d < 0
        parent = node
        setter = :"left="
        node = node.left
      elsif d > 0
        parent = node
        setter = :"right="
        node = node.right
      else
        if node.left.nil?
          if node.right.nil?
            #p :a
            parent.send(setter, nil)
          else
            #p :b
            parent.send(setter, node.right)
          end
        else
          if node.right.nil?
            #p :c
            parent.send(setter, node.left)
          else
            #p :d
            # find left most node
            parent2 = node
            setter2 = :"right="
            node2 = node.right
            while node2.left
              parent2 = node2
              setter2 = :"left="
              node2 = node2.left
            end

            node.value = node2.value
            _remove(parent2, setter2, node2, node2.value)
          end
        end
        break
      end
    end
  end

  def each
    @tree&.each do |elt|
      yield(elt)
    end
    self
  end

  def to_a
    res = []
    each do |elt|
      res << elt
    end
    res
  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, 1, x],
   [t - x, -1, x]]
}.sort
set = Set.new

min_cache = nil
cache_stale = true
i = 0
start_times.each do |d|

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

    if t <= d
      case meth
      when 1
        set.insert(x)
      when -1
        set.remove(x)
      else fail
      end
      cache_stale = true
    else
      break
    end
    i += 1
  end

  if cache_stale
    min_cache = set.min || -1
    cache_state = false
  end
  puts min_cache
end