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
EPS = 10**-7


class P2():
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self.norm2 = (self.x**2 + self.y**2)**0.5

    def __add__(self, other):
        return P2(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        return P2(self.x - other.x, self.y - other.y)

    def smul(self, a):
        return P2(self.x * a, self.y * a)

    def dot(self, other):
        return self.x * other.x + self.y * other.y

    def det(self, other):
        return self.x * other.y - self.y * other.x


n, k = map(int, input().split())
p = []
c = []
for _ in range(n):
    x, y, cc = map(float, input().split())
    p.append(P2(x, y))
    c.append(cc)

dist = [[(p[i] - p[j]).norm2 for j in range(n)] for i in range(n)]


def check(r):
    r_c = tuple(r / c[i] for i in range(n))
    # 半径rの円２つの交点の列挙
    cand = [pi for pi in p]
    for i in range(n - 1):
        for j in range(i + 1, n):
            d_ij = p[i] - p[j]

            if dist[i][j] < r_c[i] + r_c[j] - EPS:
                # 点iと点jを中心とする円が交点を持つ時
                x = ((r_c[j])**2 -
                     (r_c[i])**2 + d_ij.norm2**2) / (2 * d_ij.norm2)
                h = math.sqrt(max((r_c[j])**2 - x**2, 0.0))
                v = P2(-d_ij.y, d_ij.x).smul(h / d_ij.norm2)
                dx = p[j] + d_ij.smul(x / d_ij.norm2)
                cand.append(dx + v)
                cand.append(dx - v)

    for cand_p in cand:
        cnt = 0
        for i in range(n):
            if (p[i] - cand_p).norm2 < r_c[i] + EPS:
                cnt += 1
                if cnt >= k:
                    return True

    return False


lb = 0.0  # False
ub = 3000 * 100  # True
while ub - lb > EPS:
    mid = (ub + lb) / 2
    if check(mid):
        ub = mid
    else:
        lb = mid

print(ub)