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 PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
  list($h,$w) = explode(" ", trim(fgets(STDIN)));

  $l=[];
  $r=[];
  for($i=0;$i<$h;$i++){
    list($l[], $r[]) = explode(" ", trim(fgets(STDIN)));
  }

  $now=1;
  $zen=0;
  for($i=0;$i<$h;$i++){
    if($zen==-1){
      echo "-1".PHP_EOL;
      continue;
    }
    if($now < $l[$i]){
      $zen=$zen+1;
      $now;
    }else if($r[$i]!=$w){
      $zen=max($zen+($r[$i]-$now+2), $zen+1);
      $now=$r[$i]+1;
    }else{
      $zen=-1;
    }
    echo $zen.PHP_EOL;
  }