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 math
import sys
from itertools import combinations

stdin = sys.stdin


def ni(): return int(ns())


def na(): return list(map(int, stdin.readline().split()))


def naa(N): return [na() for _ in range(N)]


def ns(): return stdin.readline().rstrip()  # ignore trailing spaces


def circumcircle(ax, ay, bx, by, cx, cy):
    if (bx - ax) * (cy - ay) - (by - ay) * (cx - ax) == 0:
        return None
    D = 2 * (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by))
    X = ((ax * ax + ay * ay) * (by - cy) + (bx * bx + by * by)
         * (cy - ay) + (cx * cx + cy * cy) * (ay - by)) / D
    Y = ((ax * ax + ay * ay) * (cx - bx) + (bx * bx + by * by)
         * (ax - cx) + (cx * cx + cy * cy) * (bx - ax)) / D
    R = math.sqrt((X - ax) * (X - ax) + (Y - ay) * (Y - ay))
    return X, Y, R


def diametercircle(ax, ay, bx, by):
    X = (ax + bx) / 2
    Y = (ay + by) / 2
    R = math.sqrt((X - ax) * (X - ax) + (Y - ay) * (Y - ay))
    return X, Y, R


def distance(ax, ay, bx, by):
    return math.sqrt((ax - bx) ** 2 + (ay - by) ** 2)


def intersectioncircle(ax, ay, ra, bx, by, rb):
    d = distance(ax, ay, bx, by)
    if d > ra + rb:
        return None
    if d < abs(ra - rb):
        return None
    if d == 0:
        return None
    t = (ra**2 - rb**2 + d**2) / (2 * d)
    h = math.sqrt(ra**2 - t**2 + sys.float_info.epsilon)
    x2 = ax + t * (bx - ax) / d
    y2 = ay + t * (by - ay) / d
    x3 = x2 + h * (by - ay) / d
    y3 = y2 - h * (bx - ax) / d

    x4 = x2 - h * (by - ay) / d
    y4 = y2 + h * (bx - ax) / d

    return x3, y3, x4, y4


def eat_count(cx, cy, t):
    eat = 0
    for xyc in XYC_array:
        dx, dy, c = xyc
        if distance(cx, cy, dx, dy) <= (t / c + 10 ** -8):
            eat += 1
    return eat


N, K = na()
XYC_array = naa(N)


mint = 0
maxt = 10 ** 6
eps = 10 ** -6

while(maxt - mint > eps):
    t = (mint + maxt) / 2
    ok_flag = 0
    for xyc in XYC_array:
        cx, cy, _ = xyc
        if eat_count(cx, cy, t) >= K:
            ok_flag = 1
            break
    if ok_flag == 1:
        maxt = t
        continue
    for p in combinations(range(N), 2):
        ax, ay, ca = XYC_array[p[0]]
        bx, by, cb = XYC_array[p[1]]
        if intersectioncircle(ax, ay, t / ca, bx, by, t / cb):
            X1, Y1, X2, Y2 = intersectioncircle(ax, ay, t / ca, bx, by, t / cb)
            if eat_count(X1, Y1, t) >= K or eat_count(X2, Y2, t) >= K:
                ok_flag = 1
                break
    if ok_flag == 1:
        maxt = t
    else:
        mint = t

print(t)