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 PYTHON3):

Solution:
import sys
from math import sqrt
from itertools import combinations
def resolve():
    eps = 1e-7
    N, K, *xyc = map(int, sys.stdin.read().split())
    x = xyc[::3]
    y = xyc[1::3]
    ci = list(zip(x, y))
    _r = xyc[2::3]
    l = 0
    r = 10 ** 6
    while l + eps < r:
        T = (l + r) / 2
        rad = [(T/_r[i])**2 for i in range(N)]
        ans = 0
        xys = []
        for i, j in combinations(range(N), 2):
            cx1, cy1 = ci[i]
            cx2, cy2 = ci[j]
            xt = cx2-cx1
            yt = cy2-cy1
            XY = xt**2+yt**2
            a = (XY+rad[i]-rad[j])/2
            d = XY*rad[i]-a**2
            if d < eps:
                continue
            x1 = (a*xt+yt*sqrt(d))/XY+cx1
            y1 = (a*yt-xt*sqrt(d))/XY+cy1
            x2 = (a*xt-yt*sqrt(d))/XY+cx1
            y2 = (a*yt+xt*sqrt(d))/XY+cy1
            xys.append([x1, y1])
            xys.append([x2, y2])
        xys.extend(ci)
        for X, Y in xys:
            tmp = 0
            for (x, y), k in zip(ci, rad):
                if (x-X)**2+(y-Y)**2 < k+eps:
                    tmp += 1
            ans = max(ans, tmp)
            if ans >= K:
                break
        if ans >= K:
            r = T
        else:
            l = T
    print(r)
resolve()