7989: ABC255 —— B - Light It Up
[Creator : ]
Description
There are N people numbered 1,2,…,N in the xy-plane. Person i is at the coordinates $(X_i,Y_i)$.
K of these people, Persons $A_1,A_2,…,A_K$, 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.
K of these people, Persons $A_1,A_2,…,A_K$, 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:
$N\ K$
$A_1\ A_2\ …\ A_K$
$X_1\ Y_1$
$X_2\ Y_2$
$⋮$
$X_N\ Y_N$
$N\ K$
$A_1\ A_2\ …\ A_K$
$X_1\ Y_1$
$X_2\ Y_2$
$⋮$
$X_N\ Y_N$
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 $10^{−5}$.
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≤K<N≤1000
$1≤A_1<A_2<⋯<A_K≤N$
$∣X_i∣,∣Y_i∣≤10^5$
$(X_i,Y_i)\neq (X_j,Y_j)$, if i≠j.
1≤K<N≤1000
$1≤A_1<A_2<⋯<A_K≤N$
$∣X_i∣,∣Y_i∣≤10^5$
$(X_i,Y_i)\neq (X_j,Y_j)$, if i≠j.
Sample 1 Input
4 2
2 3
0 0
0 1
1 2
2 0
Sample 1 Output
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 $R≥\sqrt{5}≈2.236068$.
Every person will be lit by at least one light if $R≥\sqrt{5}≈2.236068$.
Sample 2 Input
2 1
2
-100000 -100000
100000 100000
Sample 2 Output
282842.712474619009
Sample 3 Input
8 3
2 6 8
-17683 17993
93038 47074
58079 -57520
-41515 -89802
-72739 68805
24324 -73073
71049 72103
47863 19268
Sample 3 Output
130379.280458974768