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)

(H,W),*AB = $<.map{|ln| ln.split.map(&:to_i) }

優 = [-1]*(H+1)
経 = [W]*(H+1)
h = 0 # 0..H

AB << [0,0] # AB[-1]
経 << 1 # 経[-1]
経[0] += 1

while 0 <= h
	経[h] -= 1
	next h-=1 if h == H

	l,a,b = 経[h-1],*AB[h-1]
	経[h] = a-1 if (a..b).include? 経[h]
	next h-=1 unless l <= 経[h]

	優？ = h+経[h]-経[0]
	優[h] = 優？ if 優[h] == -1 or 優？ < 優[h]
	next if 経[h+1] < 経[h]

	next 経[h+=1]+=1
end

puts 優.drop(1)