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: N, K = map(int, input().split())
  X = [list(map(int, input().split())) for i in range(N)]
  eps = 1e-12
  L, R, M, C, Yes, Y = eps, 10**6, 0, 0, 0, []
  D = [0] * N
  
  
  def dist(x, y):
      return ((x[0] - y[0]) ** 2 + (x[1] - y[1]) ** 2) ** 0.5
  
  
  def solve(E1, E2):
      Z = [
          2 * (E2[0] - E1[0]),
          2 * (E2[1] - E1[1]),
          (E1[0] + E2[0]) * (E1[0] - E2[0])
          + (E1[1] + E2[1]) * (E1[1] - E2[1])
          + (E1[2] + E2[2]) * (E2[2] - E1[2]),
      ]
      d = abs(Z[0] * E1[0] + Z[1] * E1[1] + Z[2])
      x = Z[0] * Z[0] + Z[1] * Z[1]
      r = [
          Z[1] * ((x * E1[2] * E1[2] - d * d) ** 0.5),
          Z[0] * ((x * E1[2] * E1[2] - d * d) ** 0.5),
      ]
      return [
          [((Z[0] * d - r[0]) / x) + E1[0], ((Z[1] * d + r[1]) / x) + E1[1]],
          [((Z[0] * d + r[0]) / x) + E1[0], ((Z[1] * d - r[1]) / x) + E1[1]],
      ]
  
  
  for r in range(100):
      M = (L + R) / 2
      for i in range(N):
          D[i] = M / X[i][2]
      Yes = False
      for i in range(N):
          for j in range(i + 1, N):
              if (
                  D[i] + D[j] - eps < dist(X[i], X[j])
                  or dist(X[i], X[j]) < abs(D[i] - D[j]) + eps
              ):
                  continue
              Y = solve([X[i][0], X[i][1], D[i]], [X[j][0], X[j][1], D[j]])
              for l in range(2):
                  C = 0
                  for k in range(N):
                      if (dist(X[k], Y[l]) - eps) * X[k][2] <= M:
                          C += 1
                  if C >= K:
                      Yes = True
      if Yes:
          R = M
      else:
          L = M
  print(L)
  
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"}]