题目描述
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
输入格式
见题面
输出格式
见题面