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: Accepted)

H,W = gets.split.map(&:to_i)

r = *0..W # k 段目の状態。[落水点] -> 最近蛇口位置、もしくはスキップ情報。
r[0] = 1 # 位置 0 は欠番
dmin = 0 # 横移動距離 = 落水点 - 最近蛇口位置
nmin = [0]*W
nmin[dmin] = W # r に横移動距離 0 が W 個

puts $<.map.with_index(1){|ln,k|
	next -1 if dmin < 0
	a,b = ln.split.map(&:to_i)

	i,c = a
	until b < i
		j = r[i]
		if i < j
			i = j # スキップ
		else
			c = j # 最近蛇口メモ
			nmin[i-c] -= 1 # 落水点消滅につき距離カウント減算
			i += 1
		end
	end

	if c && b+1 < (r[b+1]||b) # b+1 に新しい落水点
		r[b+1] = c
		nmin[b+1-c] += 1
	end
	r.fill([r[b+1]||b+1,b+1].max,a..b)

	dmin = (dmin...W).find{|d| 0<nmin[d] }||~k
	next k+dmin
}