A863 | Robot Instructions--Silver

Bessie is learning how to control a robot she has recently received as a gift.
The robot begins at point $(0, 0)$ on the coordinate plane and Bessie wants
the robot to end at point $(x_g, y_g)$. Bessie initially has a list of $N$
($1\le N\le 40$) instructions to give to the robot, the $i$-th of which will
move the robot $x_i$ units right and $y_i$ units up (or left or down when
$x_i$ and $y_i$ are negative, respectively).
For each $K$ from $1$ to $N$, help Bessie count the number of ways she can
select $K$ instructions from the original $N$ such that after the $K$
instructions are executed, the robot will end at point $(x_g, y_g)$.
****Note: the time and memory limits for this problem are 4s and 512MB, twice
the defaults.****

The first line contains $N$. The next line contains $x_g$ and $y_g$, each in
the range $-10^9 \ldots 10^9$. The final $N$ lines describe the instructions.
Each line has two integers $x_i$ and $y_i$, also in the range $-10^9 \ldots
10^9$.
It is guaranteed that $(x_g,y_g)\neq (0,0)$ and $(x_i,y_i)\neq (0,0)$ for all
$i$.

Print $N$ lines, the number of ways Bessie can select $K$ instructions from
the original $N$ for each $K$ from $1$ to $N$.