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 $k=i$.

4 4
2 4
1 1
2 3
2 4

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.