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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

h, w = map(int, input().split())
dic = {}
dic2 = {}
inf = float('inf')
flag = True
for i in range(h):
  a, b = map(int, input().split())
  if i == 0:
    dic[i] = {}
    for j in range(1, a):
      dic[i][j] = 1
    for j  in range(b + 1, w + 1):
      dic[i][j] = 1
    if dic[i]:
      count = 1
    else:
      count = -1
      flag = False
  else:
    #print(dic)
    if not flag:
      count = -1
    else:
      con_dic = dic.pop(i - 1)
      d_set = set()
      dic[i] = {}
      min_count = inf
      for j, v in con_dic.items():
        if a <= j and j <= b:
          d_set.add(j)
        else:
          count = v + 1
          dic[i][j] = count
          if count < min_count:
            min_count = count
      if d_set:
        max_num = max(d_set)
        k = b + 1
        if b == w:
          count = inf
        else:
          count = con_dic[max_num] + b - max_num + 2
          if count < min_count:
            min_count = count
        dic[i][k] = count
      #print(dic[i])
      if min_count == inf:
        flag = False
        count = -1
      else:
        count = min_count
  print(count)