Problem:
Score : 600 points

Problem Statement

There is a grid of squares with H+1 horizontal rows and W vertical columns.

You will start at one of the squares in the top row and repeat moving one square right or down. However, for each integer i from 1 through H, you cannot move down from the A_i-th, (A_i + 1)-th, \ldots, B_i-th squares from the left in the i-th row from the top.

For each integer k from 1 through H, find the minimum number of moves needed to reach one of the squares in the (k+1)-th row from the top. (The starting square can be chosen individually for each case.) If, starting from any square in the top row, none of the squares in the (k+1)-th row can be reached, print -1 instead.

Constraints

1 \leq H,W \leq 2\times 10^5

1 \leq A_i \leq B_i \leq W

Input

Input is given from Standard Input in the following format:

H W
A_1 B_1
A_2 B_2
:
A_H B_H

Output

Print H lines. The i-th line should contain the answer for the case k=i.

Sample Input 1

4 4
2 4
1 1
2 3
2 4

Sample Output 1

1
3
6
-1

Let (i,j) denote the square at the i-th row from the top and j-th column from the left.

For k=1, we need one move such as (1,1) → (2,1).

For k=2, we need three moves such as (1,1) → (2,1) → (2,2) → (3,2).

For k=3, we need six moves such as (1,1) → (2,1) → (2,2) → (3,2) → (3,3) → (3,4) → (4,4).

For k=4, it is impossible to reach any square in the fifth row from the top.

Solution in Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

def min(a,b); a < b ? a : b; end
def max(a,b); a > b ? a : b; end
  
INF = 1 << 28
H, W = gets.split.map(&:to_i)
T = {}
(1 .. W).each{|x| T[x] = x }

ans = (1 .. H).map do |y|
  a, b = gets.split.map(&:to_i)

  removed_keys = []
  removed_max_value = -1
  min_move = 2 * INF
  
  T.each do |k, v|
    if a <= k && k <= b
      removed_keys << k
      removed_max_value = max(removed_max_value, v)
    elsif k <= W
      min_move = min(k - v + y, min_move)
    end
  end
  
  if removed_keys.size > 0
    removed_keys.each{|k| T.delete(k) }
    if T[b + 1]
      T[b + 1] = max( T[b + 1], removed_max_value)
    else
      T[b + 1] = removed_max_value
    end
    min_move = min(y + b + 1 - T[b + 1], min_move) if b + 1 <= W
  end
  min_move >= INF ? -1 : min_move
end
puts ans