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:
from itertools import combinations

EPS = 1e-8

N, K, *XYC = map(int, open(0).read().split())
PC = [(complex(x, y), c) for x, y, c in zip(*[iter(XYC)] * 3)]


def intersection(A, r, B, s):
    D = B - A
    d = abs(D)

    cos_t = (d * d + r * r - s * s) / (2 * d * r)
    sin_t = max(1 - cos_t * cos_t, 0.0) ** 0.5

    R = r * complex(cos_t, sin_t)
    D /= d

    return (
        A + D * R,
        A + D * R.conjugate(),
    )


def is_ok(T):
    A = [p for p, _ in PC]
    for (p1, c1), (p2, c2) in combinations(PC, 2):
        A += intersection(p1, T / c1, p2, T / c2)

    for a in A:
        if K <= sum(1 for p, c in PC if c * abs(a - p) < T + EPS):
            return True
    return False


ng, ok = 0, 1000000
for _ in range(100):
    md = (ng + ok) / 2
    if is_ok(md):
        ok = md
    else:
        ng = md

print(ok)