Problem Statement

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.

Input

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

Output

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}.

Constraints

• 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 $i \neq j$.

Sample Input 1

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

Sample Output 1

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 $R \ge \sqrt{5} \approx 2.236068$.

Sample Input 2

2 1
2
-100000 -100000
100000 100000

Sample Output 2

282842.712474619009

Sample Input 3

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

Sample Output 3

130379.280458974768

见题面 Input 部分

见题面 Output 部分