Drawing

Fleeing another hostile creature from a parallel dimension, Gordon Freeman hid in a laboratory where crystals brought from the Xen dimension had once been studied. Once he realized he was in no danger, Freeman looked around and found interesting equipment built for ultra-precise drawing of complex diagrams. However, it was not designed for ordinary drawings, and its construction prevents it from drawing some of them.

On the lab computer, Freeman found blueprints of all rooms of the federal research center. Having them printed would greatly increase his chances of survival. It is not hard to guess what he decided to do!

The drawing device works as follows. An "arm" made of $n$ metal segments connected in series by hinges is fixed at a point $A_0$ on the drawing plane. Let $l_1$ be the length of the first segment (the one attached to $A_0$), $l_2$ the length of the next, and so on, up to $l_n$ for the last one. Denote the hinge point between segments $i$ and $i+1$ as $A_i$, and the end of the last segment as $A_n$. A tool that draws a point is attached at $A_n$. The control unit can place the hinge joints at points $A_i$ on the drawing plane if $|A_i A_{i+1}| = l_i$ holds for all $i < n$.

To draw the diagrams, Freeman needs to find out whether the device can draw all the required points. For each point he also needs the coordinates of every $A_i$. Help him with this.

The first line contains four integers $x_0$, $y_0$, $x_n$, $y_n$ ($-10000 \le x_0, y_0, x_n, y_n \le 10000$): the coordinates of point $A_0$, where the first segment is attached, and the coordinates of point $A_n$, the point to be drawn.

The second line contains an integer $n$ ($1 \le n \le 10^3$), the number of segments in the device. The third line contains $n$ integers $l_i$ ($1 \le l_i \le 1000$), the lengths of the segments.

The first line of the output must be YES if the point $A_n$ can be drawn, and NO otherwise. If it can be drawn, print the coordinates of $A_i$ for all $i$ from $0$ to $n$ on the next $n + 1$ lines. The answer is accepted if the distance between your points $A_i$ and $A_{i+1}$ differs from $l_i$ by no more than $10^{-3}$.