Contest: Task: Related: TaskA TaskC

Score : $200$ points

There are $N$ people numbered $1, 2, \dots, N$ in the $xy$-plane. Person $i$ is at the coordinates $(X_i, Y_i)$.

$K$ of these people, Persons $A_1, A_2, \dots, A_K$, will receive lights of the same strength.

When a person at coordinates $(x, y)$ has a light of strength $R$, it lights up the interior of a circle of radius $R$ centered at $(x, y)$ (including the boundary).

Find the minimum strength of the lights needed for every person to be lit by at least one light.

- All values in input are integers.
- $1 \le K < N \le 1000$
- $1 \le A_1 < A_2 < \dots < A_K \le N$
- $|X_i|,|Y_i| \le 10^5$
- $(X_i,Y_i) \neq (X_j,Y_j)$, if $i \neq j$.

Input is given from Standard Input in the following format:

$N$ $K$ $A_1$ $A_2$ $\dots$ $A_K$ $X_1$ $Y_1$ $X_2$ $Y_2$ $\vdots$ $X_N$ $Y_N$

Print the answer as a real number.

Your output will be considered correct if its absolute or relative error from the judge's output is at most $10^{-5}$.

4 2 2 3 0 0 0 1 1 2 2 0

2.23606797749978969

This input contains four people. Among them, Persons $2$ and $3$ will have lights.

Every person will be lit by at least one light if $R \ge \sqrt{5} \approx 2.236068$.

2 1 2 -100000 -100000 100000 100000

282842.712474619009

8 3 2 6 8 -17683 17993 93038 47074 58079 -57520 -41515 -89802 -72739 68805 24324 -73073 71049 72103 47863 19268

130379.280458974768