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

input = sys.stdin.buffer.readline

n, k = map(int, input().split())
XY = []
C = []
kouho = []
for i in range(n):
    x, y, c = map(int, input().split())
    XY.append((x, y))
    C.append(c)
    kouho.append(complex(x, y))
ct = 100
eps = 10 ** (-7)


class circle:
    def __init__(self, center, r):
        self.center = center
        self.r = r


def circle_cross(c1, c2):
    r1 = c1.r
    o1 = c1.center
    r2 = c2.r
    o2 = c2.center
    d = abs(o1 - o2)
    if d > r1 + r2:
        return 0, 0, 0
    elif r1 + r2 < d + eps and r1 + r2 > d - eps:
        # d==r1+r2
        return 1, (r2 * o1 + r1 * o2) / (r1 + r2), 0
    elif d < r1 + r2 and d > abs(r1 - r2):
        # abs(r1-r2)<d<r1+r2
        o21 = o2 - o1
        oh_nagasa = (d ** 2 + r1 ** 2 - r2 ** 2) / (2 * d)
        if oh_nagasa < eps:
            return 1, (r2 * o1 + r1 * o2) / (r1 + r2), 0
        oh = oh_nagasa * (o21 / d)
        housen = (o21 / d) * complex(0, 1)
        suisen = max(0, (r1 ** 2 - oh_nagasa ** 2) ** (1 / 2))
        ans1 = o1 + oh + housen * suisen
        ans2 = o1 + oh - housen * suisen
        return 2, ans1, ans2
    elif abs(r1 - r2) > d - eps and abs(r1 - r2) < d + eps:
        # d=abs(r1-r2)
        ans = (-r2 * o1 + r1 * o2) / (r1 - r2)
        return 1, ans, 0
    else:
        # d<abs(r1-r2)
        return 0, 0, 0


if n == 1:
    print(0)
    exit()
if k == 1:
    print(0)
    exit()

ok = 10 ** 10
ng = 0

while ct > 0:
    mid = (ok + ng) / 2
    kouho_temp = kouho[::]
    for i in range(n - 1):
        a, b = XY[i]
        p = C[i]
        A = circle(complex(a, b), mid / p)
        for j in range(i + 1, n):
            c, d = XY[j]
            q = C[j]
            B = circle(complex(c, d), mid / q)
            t1, t2, t3 = circle_cross(A, B)
            if t1 == 0:
                continue
            if t1 == 1:
                kouho_temp.append(t2)
            if t1 == 2:
                kouho_temp.append(t2)
                kouho_temp.append(t3)
    res = 0
    for z in kouho_temp:
        cnt = 0
        for i in range(n):
            x, y = XY[i]
            p = C[i]
            z1 = complex(x, y)
            if abs(z - z1) < mid / p + eps:
                cnt += 1
        res = max(cnt, res)
    if res >= k:
        ok = mid
    else:
        ng = mid
    ct -= 1


print(mid)