Problem:
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Cross Points of a Circe and a Line

For given a circle $c$ and a line $l$, print the coordinates of the cross points of them.

Input

The input is given in the following format.

$cx\; cy\; r$

$q$

$Line_1$

$Line_2$

:

$Line_q$

In the first line, the center coordinate of the circle and its radius are given by $cx$, $cy$ and $r$. In the second line, the number of queries $q$ is given.

In the following $q$ lines, as queries, $Line_i$ are given ($1 \leq i \leq q$) in the following format.

$x_1\; y_1\; x_2\; y_2$

Each line is represented by two points $p1$ and $p2$ which the line crosses. The coordinate of $p1$ and $p2$ are given by ($x1$, $y1$) and ($x2$, $y2$) respectively. All input values are given in integers.

Output

For each query, print the coordinates of the cross points in the following rules.

If there is one cross point, print two coordinates with the same values.

Print the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.

The output values should be in a decimal fraction with an error less than 0.000001.

Constraints

$p1$ and $p2$ are different

The circle and line have at least one cross point

$1 \leq q \leq 1,000$

$-10,000 \leq cx, cy, x1, y1, x2, y2 \leq 10,000$

$1 \leq r \leq 10,000$

Sample Input and Output

Sample Input

2 1 1
2
0 1 4 1
3 0 3 3

Sample Output

1.00000000 1.00000000 3.00000000 1.00000000
3.00000000 1.00000000 3.00000000 1.00000000

Solution in Ruby (judge verdict: Wrong Answer)

require 'matrix'

cx, cy, r = gets.split.map &:to_i
c = Vector[ cx, cy ]
q = gets.to_i
q.times do
  x1, y1, x2, y2 = gets.split.map &:to_i
  p0 = Vector[ x1, y1 ]
  p1 = Vector[ x2, y2 ]
  p0pr_norm = (c - p0).inner_product(p1 - p0).abs / (p1 - p0).norm
  p0p1_base = (p1 - p0) / (p1 - p0).norm
  pr = p0 + p0p1_base * p0pr_norm
  x = ( r**2 - (c - pr).norm**2 ) ** (1/2.0)
  i1 = pr - p0p1_base * x
  i2 = pr + p0p1_base * x
  puts "%.6f %.6f %.6f %.6f" % [ i1[0], i1[1], i2[0], i2[1] ]
end