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)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function calc(x1,y1,r1,x2,y2,r2)
	if x1==x2
		y = ((y1^2-y2^2)-(r1^2-r2^2))/(2*(y1-y2))
		a = 1
		b = 2*x1
		c = x1^2-r1^2-(y-y1)^2
		[((-b+sqrt(b^2-4*a*c))/(2*a),y),((-b-sqrt(b^2-4*a*c))/(2*a),y)]
	elseif y1==y2
		x = ((x1^2-x2^2)-(r1^2-r2^2))/(2*(x1-x2))
		a = 1
		b = 2*y1
		c = y1^2-r1^2-(x-x1)^2
		[(x,(-b+sqrt(b^2-4*a*c))/(2*a)),(x,(-b-sqrt(b^2-4*a*c))/(2*a))]
	else
		a = ((x1-x2)^2+(y1-y2)^2)/((y1-y2)^2)
		b = ((x1-x2)*(x1^2-x2^2)-(y1-y2)^2*(3*x1-x2)-(r1^2-r2^2)*(x1-x2))/((y1-y2)^2)
		c = ((x1^2-x2^2)-(y1-y2)^2-(r1^2-r2^2))^2/(4*(y1-y2)^2)-r1^2+x1^2
		xa = (b+sqrt(b^2-4*a*c))/(2*a)
		xb = (b-sqrt(b^2-4*a*c))/(2*a)
		[(xa,((x1^2-x2^2)+(y1^2-y2^2)-(r1^2-r2^2)-2*(x1-x2)*xa)/(2*(y1-y2))),(xb,((x1^2-x2^2)+(y1^2-y2^2)-(r1^2-r2^2)-2*(x1-x2)*xb)/(2*(y1-y2)))]
	end
end

function main()
	n,k = readline() |> split |> parseMap
	a = Tuple{Int,Int,Int}[(0,0,0) for i in 1:n]
	for i in 1:n
		x,y,c = readline() |> split |> parseMap
		a[i] = (x,y,c)
	end
	l = -1.0
	r = 100001.0
	for iter in 1:10000
		m = (l+r)/2
		lis = Tuple{Float64,Float64}[]
		for i in 1:n-1
			for j in i+1:n
				x1=a[i][1]
				y1=a[i][2]
				r1=m/a[i][3]
				x2=a[j][1]
				y2=a[j][2]
				r2=m/a[j][3]
				if r1+r2>sqrt((x1-x2)^2+(y1-y2)^2)&&sqrt((x1-x2)^2+(y1-y2)^2)+min(r1,r2)>max(r1,r2)
					(za,zb) = calc(x1,y1,r1,x2,y2,r2)
					push!(lis,za)
					push!(lis,zb)
				end
			end
		end
		f = 0
		for z in lis
			x = 0
			for i in 1:n
				x1=a[i][1]
				y1=a[i][2]
				r1=m/a[i][3]
				if (x1-z[1])^2+(y1-z[2])^2<r1^2
					f += 1
				end
			end
			if x<k
				f = 1
			end
		end
		if f==0
			l = m
		else
			r = m
		end
	end
	println(r)
end

main()