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}.

-----Sample Input----- 4 3 -1 0 3 0 0 3 1 0 2 1 1 40

-----Sample Output----- 2.4

If we put the heat source at \left(-0.2, 0\right), the 1-st, 2-nd, and 3-rd pieces of meat will be ready to eat within 2.4 seconds. This is the optimal place to put the heat source.