output_description: Print the answer.
  
  It will be considered correct if its absolute or relative error from our
  answer is at most 10^{-6}.
  
  * * *
input_description: 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
attempt: import math
  
  n, k = map(int, input().split())
  xyc = [list(map(int, input().split())) for i in range(n)]
  
  
  def time(p, q):
      ls = []
      for x, y, c in xyc:
          ls.append(math.hypot(x - p, y - q) * c)
      ls.sort()
      return ls[k - 1]
  
  
  def tsearch(u):
      lx = -1000
      rx = 1000
      for _ in range(100):
          mlx = lx * (2 / 3) + rx * (1 / 3)
          mrx = lx * (1 / 3) + rx * (2 / 3)
          if time(mlx, u) > time(mrx, u):
              lx = mlx
          else:
              rx = mrx
      return lx
  
  
  ly = -1000
  ry = 1000
  for _ in range(100):
      mly = ly * (2 / 3) + ry * (1 / 3)
      mry = ly * (1 / 3) + ry * (2 / 3)
      if tsearch(mly) > tsearch(mry):
          ly = mly
      else:
          ry = mry
  lx = tsearch(ly)
  print(time(lx, ly))
  
problem_description: Statement
  
  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.
samples: [{"input": "4 3\n    -1 0 3\n    0 0 3\n    1 0 2\n    1 1 40", "output": "2.4\n    \n\nIf we put the heat source at \\left(-0.2, 0\\right), the 1-st, 2-nd, and 3-rd\npieces of meat will be ready to eat within 2.4 seconds. This is the optimal\nplace to put the heat source.\n\n* * *"}, {"input": "10 5\n    -879 981 26\n    890 -406 81\n    512 859 97\n    362 -955 25\n    128 553 17\n    -885 763 2\n    449 310 57\n    -656 -204 11\n    -270 76 40\n    184 170 16", "output": "7411.2252"}]