Problem: 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}.

Examples

Input

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


Output

2.4


Input

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


Output

7411.2252

Solution (in PYTHON):

Solution:
import sys,math
range = xrange
input = raw_input

inp = [int(x) for x in sys.stdin.read().split()]; ii = 0

n = inp[ii]; ii += 1
k = inp[ii]; ii += 1

X = inp[ii + 0: ii + 3 * n: 3]
Y = inp[ii + 1: ii + 3 * n: 3]
C = inp[ii + 2: ii + 3 * n: 3]
ii += 3 * n

def dist(i,j):
    return math.sqrt((X[i] - X[j])**2 + (Y[i] - Y[j])**2)

l = 0.0
r = 100.0 * 1e18
while r - l >= 1e-9:
    t = (l + r) / 2

    R = [t/C[i] for i in range(n)]

    cand = [(X[i], Y[i]) for i in range(n)]

    for i in range(n):
        r0 = R[i]
        x0 = X[i]
        y0 = Y[i]
        for j in range(i):
            r1 = R[j]
            x1 = X[j]
            y1 = Y[j]

            d = dist(i,j)
            if d == 0.0:
                continue
            a = (r0**2 - r1**2 + d**2)/(2*d)
            if 0.0 < d <= r0 + r1 and r0**2 - a**2 >= 0.0:
                h = math.sqrt(r0**2 - a**2)

                x2 = x0 + a * (x1 - x0)/d
                y2 = y0 + a * (y1 - y0)/d
                #cand.append((x2,y2))

                x3 = x2 + h * (y1 - y0)/d
                y3 = y2 - h * (x1 - x0)/d
                cand.append((x3,y3))
                
                x3 = x2 + h * (y1 - y0)/d
                y3 = y2 - h * (x1 - x0)/d
                cand.append((x3,y3))

    for x,y in cand:
        count = 0
        for i in range(n):
            if math.sqrt((X[i] - x)**2 + (Y[i] - y)**2) <= R[i] + 1e-9:
                count += 1

        if count >= k:
            r = t
            break
    else:
        l = t
print (l + r)/2