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: Wrong Answer)

H, W = gets.split.map(&:strip).map(&:to_i)
A = Array.new(H)
B = Array.new(H)
H.times do |i|
  A[i], B[i] = gets.split.map(&:strip).map(&:to_i)
end

M = 10**6
INF = 10**10


def solve(k)
  m = Array.new(W, 0)
  w = (1..W).to_a
  ii = W
  vk = 1
  while vk <= k
    i = 0
    while w[i] < A[vk-1]
      i += 1
    end
    if B[vk-1] == W
      ii = i
    elsif i < ii
      if w[i] <= B[vk-1]
        w[i] = B[vk-1] + 1
        i += 1
        j = i
        while j < ii && w[j] <= B[vk-1]
          j += 1
        end
        while j < ii
          w[i] = w[j]
          i+= 1
          j+= 1
        end
        ii = i
      end
    end
    if ii > 0
      ans = w[0...ii].min_by.with_index{|w,i| w-i} -1 + vk
      if ans < INF
        puts ans
      else
        puts -1
      end
    else
      puts -1
    end
    vk += 1
  end
end

solve(H)