Score : $600$ points
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.
Input is given from Standard Input in the following format:
$H$ $W$ $A_1$ $B_1$ $A_2$ $B_2$ $:$ $A_H$ $B_H$
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.