Problem Statement

There are N lines in a two-dimensional plane. The i-th line is A_i x + B_i y + C_i = 0. It is guaranteed that no two of the lines are parallel.
In this plane, there are $\frac{N(N-1)}{2}$ intersection points of two lines, including duplicates. Print the distance between the origin and the K-th nearest point to the origin among these $\frac{N(N-1)}{2}$ points.

Input

Input is given from Standard Input in the following format:
N K
A_1 B_1 C_1
A_2 B_2 C_2
$\vdots$
A_N B_N C_N

Output

Print a real number representing the answer.
Your output is considered correct when its absolute or relative error from the judge's output is at most 10^{-4}.

Constraints

• $2 \le N \le 5 \times 10^4$
• $1 \le K \le \frac{N(N-1)}{2}$
• -$1000 \le |A_i|,|B_i|,|C_i| \le 1000(1 \le i \le N)$
• No two of the lines are parallel.
• $A_i \neq 0$ or $B_i \neq 0(1 \le i \le N)$.
• All values in input are integers.

Sample Input 1

3 2
1 1 1
2 1 -3
1 -1 2

Sample Output 1

2.3570226040

Let us call the i-th line Line i.

• The intersection point of Line 1 and Line 2 is (4,-5), whose distance to the origin is $\sqrt{41} \simeq 6.4031242374$.
• The intersection point of Line 1 and Line 3 is $(\frac{-3}{2},\frac{1}{2}),$ whose distance to the origin is $\frac{\sqrt{10}}{2} \simeq 1.5811388300$.
• The intersection point of Line 2 and Line 3 is $(\frac{1}{3},\frac{7}{3}),$ whose distance to the origin is $\frac{5\sqrt{2}}{3} \simeq 2.3570226040$.

Therefore, the second nearest intersection point is $(\frac{1}{3},\frac{7}{3})$, and $\frac{5\sqrt{2}}{3}$ should be printed.

Sample Input 2

6 7
5 1 9
4 4 -3
8 -1 2
0 1 -8
4 0 -4
2 -3 0

Sample Output 2

4.0126752298

见题面 Input 部分

见题面 Output 部分