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 Heap
  def initialize(n)
    @nodes = Array.new(n)
    @index = Hash.new
    @size = 0
  end

  def push(current_value)
    current_index = @size
    @size += 1

    while current_index > 0 do
      parent_index = (current_index - 1)>>1
      parent_value = @nodes[parent_index]
      break if parent_value <= current_value

      @index[parent_value] = current_index
      @nodes[current_index] = parent_value
      current_index = parent_index
    end
    @index[current_value] = current_index
    @nodes[current_index] = current_value
  end

  def delete(delete_target_value)
    return unless @index[delete_target_value]
    @size -= 1
    current_node_value = @nodes.delete_at(@size) # delete_atの返り値は、削除した値
    current_node_index = @index.delete(delete_target_value) # delteの返り値は削除した値

    # 削除したのがそもそも末端だったら、終了。
    return if current_node_index == @size

    # 削除したのが末端じゃないなら、末端にある値を削除した場所に持ってくる
    @nodes[current_node_index] = current_node_value
    @index[current_node_value] = current_node_index

    if delete_target_value > current_node_value
      parent_node_index = (current_node_index - 1) >> 1
      while @nodes[parent_node_index]&.> @nodes[current_node_index]
        change(parent_node_index, current_node_index)
        current_node_index = parent_node_index
        current_node_value = @nodes[current_node_index]
        parent_node_index = (current_node_index - 1) >> 1
      end
    else
      while
        # 子ノードのindexを取得、小さい方(左)のindexがsize以上だったら、そこに要素は無いはずなのでbreak
        child_node_index_r = (current_node_index << 1) + 2
        child_node_index_l = child_node_index_r - 1
        break unless child_node_index_l < @size

        child_node_value_l = @nodes[child_node_index_l]
        child_node_value_r = @nodes[child_node_index_r]
        if child_node_value_r&.<child_node_value_l
          min_child_value = child_node_value_r
          min_child_index = child_node_index_r
        else
          min_child_value = child_node_value_l
          min_child_index = child_node_index_l
        end
        break if min_child_value > current_node_value

        # 入れ替えた後、現在のindexを入れ替え先のindexにして、次のloopへ行く
        change(current_node_index, min_child_index)
        current_node_index = min_child_index
      end
    end
  end

  def top
    @size == 0 ? -1 : @nodes[0]
  end

  private

  def change(index_i, index_j)
    @nodes[index_i], @nodes[index_j] = @nodes[index_j], @nodes[index_i]
    @index[@nodes[index_i]] = index_i
    @index[@nodes[index_j]] = index_j
  end
end

nn, qq = gets.split.map(&:to_i)
events = []
temp = []

t = 0
nn.times do
  temp = gets.split.map(&:to_i)
  next if (t = temp[1] - temp[2]) <= 0

  events.push(
    ((temp[0] - temp[2]) << 32) +
    (2 << 30) +
    temp[2]
  )
  events.push(
    (t << 32) +
    temp[2]
  )
end

1.step(qq, 1) do |i|
  events.push(
    (gets.to_i << 32) +
    (3 << 30) +
    i
  )
end

# '30bit-2bit-30bit'
#  ソートするための区間 - タイプ - indexなどの情報
mask_point = ((1 << 30) - 1)
mask_index = ((1 << 18) - 1)

events.sort!

ss = Heap.new(nn)
ans = []

events.each do |event|
  if event[30] == 0
    if event[31] == 1
      ss.push(event & mask_point)
    else
      ss.delete(event & mask_point)
    end
  else
    ans[(event & mask_index)] = ss.top
  end
end

puts ans[1..-1]