Contest Duration: - (local time) (100 minutes) Back to Home
F - Yakiniku Optimization Problem /

Time Limit: 2 sec / Memory Limit: 1024 MB

制約

• 入力は全て整数
• 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

入力

N K
x_1 y_1 c_1
\vdots
x_N y_N c_N


出力

なお、想定解答との絶対誤差または相対誤差が 10^{-6} 以下であれば正解として扱われる。

入力例 1

4 3
-1 0 3
0 0 3
1 0 2
1 1 40


出力例 1

2.4


入力例 2

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


出力例 2

7411.2252


Score : 600 points

Problem 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.

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

It will be considered correct if its absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

4 3
-1 0 3
0 0 3
1 0 2
1 1 40


Sample Output 1

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.

Sample Input 2

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


Sample Output 2

7411.2252