Problem:
Score : 600 points

Problem Statement

Takahashi wants to grill N pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the i-th piece of meat are \left(x_i, y_i\right), and its hardness is c_i.

Takahashi can use one heat source to grill the meat. If he puts the heat source at coordinates \left(X, Y\right), where X and Y are real numbers, the i-th piece of meat will be ready to eat in c_i \times \sqrt{\left(X - x_i\right)^2 + \left(Y-y_i\right)^2} seconds.

Takahashi wants to eat K pieces of meat. Find the time required to have K or more pieces of meat ready if he put the heat source to minimize this time.

Constraints

All values in input are integers.

1 \leq N \leq 60

1 \leq K \leq N

-1000 \leq x_i , y_i \leq 1000

\left(x_i, y_i\right) \neq \left(x_j, y_j\right) \left(i \neq j \right)

1 \leq c_i \leq 100

Input

Input is given from Standard Input in the following format:

N K
x_1 y_1 c_1
\vdots
x_N y_N c_N

Output

Print the answer.

It will be considered correct if its absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

4 3
-1 0 3
0 0 3
1 0 2
1 1 40

Sample Output 1

2.4

If we put the heat source at \left(-0.2, 0\right), the 1-st, 2-nd, and 3-rd pieces of meat will be ready to eat within 2.4 seconds. This is the optimal place to put the heat source.

Sample Input 2

10 5
-879 981 26
890 -406 81
512 859 97
362 -955 25
128 553 17
-885 763 2
449 310 57
-656 -204 11
-270 76 40
184 170 16

Sample Output 2

7411.2252

Solution in Julia (0.5.0) (judge verdict: Runtime Error)

const N,K=map(x->parse(Int,x),split(readline()))
const X=Float64[]
const Y=Float64[]
const C=Float64[]
for _=1:N
	x,y,c=map(x->parse(Float64,x),split(readline()))
	push!(X,x)
	push!(Y,y)
	push!(C,c)
end
function check(M)
	A=Pair{Float64,Float64}[]
	for i=1:N
		push!(A,X[i]=>Y[i])
	end
	r=[M/c for c=C]
	for i=1:N,j=i+1:N
		d=sqrt((X[i]-X[j])^2+(Y[i]-Y[j])^2)
		ri=r[i]
		rj=r[j]
		if d<abs(ri-rj)||ri+rj<d
			continue
		end
		a=acos((ri^2+d^2-rj^2)/(2*ri*d))
		t=atan(Y[j]-Y[i],X[j]-X[i])
		push!(A,X[i]+ri*cos(t+a)=>Y[i]+ri*sin(t+a))
		push!(A,X[i]+ri*cos(t-a)=>Y[i]+ri*sin(t-a))
	end
	ret=false;
	for (x,y)=A
		cnt=0
		for i=1:N
			if sqrt((X[i]-x)^2+(Y[i]-y)^2)<=r[i]+1e-10
				cnt+=1
			end
		end
		if cnt>=K
			ret=true
		end
	end
	ret
end
function main()
	L=0
	R=1e9
	for _=1:100
		M=(L+R)/2
		if check(M)
			R=M
		else
			L=M
		end
	end
	println(R)
end
main()