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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

N,K = map(int,input().split())
xyc = [list(map(int,input().split())) for _ in range(N)]

def cir_line_intersection(x0,y0,r,a,b,c):
    res = []
    c = c-a*x0-b*y0
    x = x0+(a*c+b*((a**2+b**2)*r**2-c**2)**0.5)/(a**2+b**2)
    y = y0+(b*c-a*((a**2+b**2)*r**2-c**2)**0.5)/(a**2+b**2)
    res.append([x,y])
    x = x0+(a*c+b*((a**2+b**2)*r**2-c**2)**0.5)/(a**2+b**2)
    y = y0+(b*c-a*((a**2+b**2)*r**2-c**2)**0.5)/(a**2+b**2)
    res.append([x,y])
    return res

def cir2_intersection(x1,y1,r1,x2,y2,r2):
    a = 2*(x1-x2)
    b = 2*(y1-y2)
    c = -r1**2+r2**2+x1**2-x2**2+y1**2-y2**2
    return cir_line_intersection(x1,y1,r1,a,b,c)

def burn(t):
    cand = []
    for i in range(N):
        x1,y1,c1 = xyc[i]
        r1 = t/c1
        cand.append([x1,y1])
        for j in range(i+1,N):
            x2,y2,c2 = xyc[j]
            r2 = t/c2
            r = ((x1-x2)**2+(y1-y2)**2)**0.5
            if abs(r1-r2)<=r<=r1+r2:
                cand += cir2_intersection(x1,y1,r1,x2,y2,r2)
    res = False
    for x,y in cand:
        cnt = 0
        for i in range(N):
            x1,y1,c1 = xyc[i]
            if t>=c1*((x-x1)**2+(y-y1)**2)**0.5:
                cnt += 1
        if cnt>=K:
            res = True
            break

    return res

ng = 0
ok = 300000
m = (ok+ng)/2
for i in range(40):
    if burn(m):
        ok = m
    else:
        ng = m
    m = (ok+ng)/2
print(m)