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:
N, K = map(int, input().split())
xyc = [[int(i) for i in input().split()] for _ in range(N)]

def check(n) :
  for i in range(N) :
    xi, yi, ci = xyc[i]
    ri = n / ci
    for j in range(i + 1, N) :
      xj, yj, cj = xyc[j]
      xj -= xi
      yj -= yi
      rj = n / cj
      a = (xj ** 2 + yj ** 2 + ri ** 2 - rj ** 2) / 2
      root = max(0, (xj ** 2 + yj ** 2) * (ri ** 2) - a ** 2) ** 0.5
      for sgn in [1, -1] :
        cnt = 0
        X = (a * xj + sgn * yj * root) / (xj ** 2 + yj ** 2) + xi
        Y = (a * yj - sgn * xj * root) / (xj ** 2 + yj ** 2) + yi
        for x, y, c in xyc :
          if (x - X) ** 2 + (y - Y) ** 2 <= (n / c) ** 2 + eps :
            cnt += 1
        if cnt >= K :
          return True
  
  for X, Y, _ in xyc :
    cnt = 0
    for x, y, c in xyc :
      if (x - X) ** 2 + (y - Y) ** 2 <= (n / c) ** 2 + eps :
        cnt += 1
    if cnt >= K :
      return True
      
  return False

eps = 1e-8
ng, ok = 0, 10 ** 6
while ok - ng > eps :
  n = (ng + ok) / 2
  if check(n) :
    ok = n
  else :
    ng = n
 
print(ok)