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 itertools import combinations
from math import sqrt

read = sys.stdin.read
readline = sys.stdin.readline


def main():
    N, K, *xyc = map(int, read().split())
    x = xyc[::3]
    y = xyc[1::3]
    xy = list(zip(x, y))
    c = xyc[2::3]
    left = 0
    right = 10 ** 6
    delta = 0.1 ** 7
    while right - left > delta:
        mid = (left + right) / 2
        intersections = []
        r = [(mid / i) ** 2 for i in c]
        for i, j in combinations(range(N), 2):
            x1, y1 = xy[i]
            x2, y2 = xy[j]
            X = x2 - x1
            Y = y2 - y1
            XY = X ** 2 + Y ** 2
            r1 = r[i]
            r2 = r[j]

            a = (XY + r1 - r2) / 2
            b = XY * r1 - a ** 2
            if b < delta:
                continue
            b = sqrt(b)
            xi1 = (a * X + Y * b) / XY + x1
            yi1 = (a * Y - X * b) / XY + y1
            xi2 = (a * X - Y * b) / XY + x1
            yi2 = (a * Y + X * b) / XY + y1
            intersections.append((xi1, yi1))
            intersections.append((xi2, yi2))

        intersections.extend(xy)
        cnt = 0
        for X, Y in intersections:
            tmp = 0
            for (i, j), k in zip(xy, r):
                XY = (X - i) ** 2 + (Y - j) ** 2
                if XY < k + delta:
                    tmp += 1
            cnt = max(tmp, cnt)
            if cnt >= K:
                break
        if cnt >= K:
            right = mid
        else:
            left = mid

    print(right)


if __name__ == '__main__':
    main()