Light

Péter has a large garden with $N$ Christmas trees. Out of these, he selects $K$ trees, each of which is illuminated with a bulb of strength $S$ . A bulb with strength $S$ provides light intensity $\frac{S}{d^2}\$ at a distance $d$ . At any point in the garden, the light intensities of the illuminated trees add up. Péter wants to know the smallest positive integer $S$ such that at all unlit trees, the light intensity is at least 1.

Let’s help him calculate this!

Input specification

The first line contains $N$ and $K$ . The next $N$ lines contain the coordinates $x_i$ and $y_i$ of the trees ( $i=1...N$ ). Finally, the last line contains $K$ numbers: the indices of the illuminated trees. All numbers are integers, and the numbers on the same line are separated by spaces.

Output specification

A single line with the required number $S$ .

Constraints

$1\le N \le 1\_000$
$1\le K \le 1\_000$
$-10\_000\le x_i,y_i \le 10\_000$
The numbers in the input are integers and the points $x_{i},y_{i}$ are pairwise different and $K$ is always smaller than $N$ .