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:
#!/usr/bin/env python3
import sys
input = sys.stdin.readline
import math
eps = 1e-12

def calc_intersection_points(circle0, circle1):
    x0, y0, r0 = circle0
    x1, y1, r1 = circle1
    d = math.hypot(x0 - x1, y0 - y1)
    if d > r0 + r1 or d < abs(r0 - r1):
        return []
    ret = []
    if r0 + r1 == d:
        a = r0
        h = 0.0
    else:
        a = (r0**2 - r1**2 + d**2) / (2.0 * d)
        h = math.sqrt(r0**2 - a**2)
    x2 = x0 + a * (x1 - x0) / d
    y2 = y0 + a * (y1 - y0) / d
    x3 = x2 + h * (y1 - y0) / d
    y3 = y2 - h * (x1 - x0) / d
    ret.append((x3, y3))
    if h == 0:
        return ret
    x4 = x2 - h * (y1 - y0) / d
    y4 = y2 + h * (x1 - x0) / d
    ret.append((x4, y4))
    return ret


n, k = map(int, input().split())
niku = []
for _ in range(n):
    x, y, c = map(int, input().split())
    niku.append((x, y, c))

l = 0.0; r = 10**8
for _ in range(64):
    mid = (l + r) / 2.0
    circles = []
    for x, y, c in niku:
        circles.append((x, y, mid / c))
    points = []
    for i in range(n):
        for j in range(i+1, n):
            points += calc_intersection_points(circles[i], circles[j])
    for x, y, _ in niku:
        points.append((x, y))
    cooked = 0
    for x, y in points:
        ret = 0
        for cx, cy, cr in circles:
            if math.hypot(x - cx, y - cy) <= cr + eps:
                ret += 1
        if ret > cooked:
            cooked = ret
    if cooked >= k:
        r = mid
    else:
        l = mid
print(l)