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.

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.

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 $10^{-4}$.

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