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 $k=i$.