# Problem K

Within Arm's Reach

João wants to join the robotic football team of his university. However, since he knows little about robotics and mathematics, he decided to build a $2$-dimensional robotic arm to bootstrap his knowledge.

The robotic arm is composed of $N$ segments of various lengths. The segments can form any angle between them, including configurations that make it appear to self-intersect when viewed from above. The robotic arm works great, but it is not trivial to position the arm’s tip as close as possible to given $x$, $y$ target coordinates with so many joints to control. Can you help João?

## Task

Given the robotic arm description and target coordinates relative to the arm’s origin, calculate a configuration that places the arm’s tip as close as possible to the target.

## Input

The first line contains $N$, the number of segments composing the robotic arm. $N$ lines follow, each with an integer $L_ i$ describing the length of the $i$th segment from the fixed point until the arm’s tip. There is one more line with $2$ integers: the $x$, $y$ coordinates of the target point to reach.

## Constraints

$1$ |
$\leq $ |
$N$ |
$\leq $ |
$20$ |
Number of segments in the robotic arm |

$1$ |
$\leq $ |
$L_ i$ |
$\leq $ |
$1\, 000$ |
Length of the $i$th segment |

$-20\, 000$ |
$\leq $ |
$x, y$ |
$\leq $ |
$20\, 000$ |
Target coordinates to attempt to reach |

## Output

The output should contain $N$ lines, each containing two real numbers $x_ i$, $y_ i$ indicating the coordinates of the tip of the $i$th segment.

The length of the $i$th segment computed from the solution and input $L_ i$ may not differ by more than $0.01$. Similarly, the absolute error between the solution’s distance to the target and the minimum possible distance to the target cannot exceed $0.01$.

Note that, in general, there are many solutions. Your program may output any of them.

## Explanation for Sample Input 1

Sample output 1 corresponds to the drawing on the left:

The drawing on the right corresponds to the following, equally acceptable output for sample input 1:

3.923 3.100 1.118 2.037 5.000 3.000

## Explanation for Sample Input 2

Sample Input 1 | Sample Output 1 |
---|---|

3 5 3 4 5 3 |
4.114 -2.842 6.297 -0.784 5.000 3.000 |

Sample Input 2 | Sample Output 2 |
---|---|

2 4 2 -8 -3 |
-3.745 -1.404 -5.618 -2.107 |