\begin{problem}{Painting}{painting.in}{painting.out}{2 sec}{256 Mb}

%Автор задачи: Борис Минаев
%Автор условия: Борис Минаев

Dr. Freeman has a device for drawing diagrams. At some point of the plane $A_0$ there is a hand, consisting 
of $n$ segments, connected by hinges. The length of the first segment (the one attached to the point of $A_0$) 
as $l_1$, next $l_2$, ..., the last $l_n$. Denote the junction of segments with numbers $i$ and $i + 1$
as $A_i$, and the end of the last segment as $A_n$. 

At the point of $A_n$ the tool is mounted that allows you to draw a point. 
The control unit can place the joints at the points $A_i$ in the plane of 
the paper, if for all $1\le i < n$ the distance $|A_i A_{i+1}| = l_i$.

Freeman wants to draw point. Help him to set the device in the position
in which he can do it. 
        
\InputFile
The first line of the input file contains four integers $x_0$, $y_0$, 
$x_n$, $y_n$ ($-10{\,}000 \le x_0, y_0, x_n, y_n \le 10{\,}000$), the coordinates 
of point $A_0$, where the first segment is attached and the point $A_n$ you need to draw.

The next line contains an integer $n$ ($1\le n \le 10^3$), the number of segments in 
the paint device. The next line contains $n$ integers $l_i$ ($1\le l_i \le 1{\,}000$), the length of segments.

\OutputFile

Output the word \texttt{YES}, if it is possible to draw a point $A_n$ and \texttt{NO} otherwise. 
If answer is positive, then output in the next $n + 1$ lines the coordinates of points $A_i$ 
for all $i$ from zero to $n$. The answer will be accepted if the distance between the points
$A_i$ and $A_{i + 1}$ is different from $l_i$ no more than $10^{-3}$.

\Examples
\begin{example}%
\exmp{
0 0 6 0
2
5 5
}{
YES
0.000 0.000
3.000 4.000
6.000 0.000
}%
\end{example}

\Note
The number of tests in which $\sum_1^{n}l_i$ does not exceed the distance from $A_0$ to $A_n$, is 20\% of all tests.

The number of tests in which $n \le 2$, is 40\% of all tests.

\end{problem}

