Problem Statement

The Black-Tailed Gull and her companions are about to fight a Cerulean (monster).

Simply put, the Black-Tailed Gull's standby skill makes the opponent unable to act (under certain conditions). How unfair!

However, the skill does not activate if the Black-Tailed Gull herself acts, and its activation chance is halved if there is a Friend who acts multiple times.

$N$ Friends fight a Cerulean.

The Friends are numbered $1,2,\dots,N$, and Friend $X$ is the Black-Tailed Gull. No other Friend is the Black-Tailed Gull.

The battle lasts for $Q$ turns. In turn $i$, $M_i$ actions are performed. Specifically, Friends $F_{i,1},F_{i,2}\dots,F_{i,M_i}$ act in this order.

Whether the Cerulean acts in turn $i$ is determined as follows.

• If the Black-Tailed Gull acted at least $1$ time in turn $i$, the Cerulean always acts $1$ time.
• Otherwise, if there is a Friend who acted $2$ or more times in turn $i$, the Cerulean acts $1$ time with probability $\frac{1}{2}$ and does not act with probability $\frac{1}{2}$.
• If neither of the above applies, the Cerulean never acts.

Find the expected number of times the Cerulean acts. Whether the Cerulean acts is determined independently for each turn. Also, both the Friends and the Cerulean are sufficiently strong, and none of them will be defeated before $Q$ turns have passed.

Constraints

• $1\leq X\leq N\leq 10^9$
• $1\leq Q$
• $1\leq M_i$
• $\sum_{i=1}^{Q}M_i\leq 2\times 10^5$
• $1\leq F_{i,j}\leq N$
• All input values are integers.

Input

$N$ $X$ $Q$
$M_1$
$F_{1,1}$ $F_{1,2}$ $\dots$ $F_{1,M_1}$
$M_2$
$F_{2,1}$ $F_{2,2}$ $\dots$ $F_{2,M_2}$
$\vdots$
$M_Q$
$F_{Q,1}$ $F_{Q,2}$ $\dots$ $F_{Q,M_Q}$

Output

Output the answer. Your answer is judged as correct if its absolute or relative error from the correct answer is at most $10^{-5}$.

Sample

10 1 3
3
1 2 1
3
3 3 4
3
9 2 4

1.5

5 2 4
3
1 3 4
3
3 5 4
4
5 4 1 3
3
3 1 4

0