Simple Polygon

You are given two integers, the number of vertices $N$ and area $A$. You need to construct a simple polygon of $N$ vertices such that the area of the polygon is exactly $\frac{A}{2}$, and all the vertices have non-negative integer coordinates with value up to $10^9$.

A simple polygon is one that:

• Defines a closed area.
• Does not have self-intersections, even at a single point.
• No two consecutive edges form a straight angle.

The first line of the input gives the number of test cases, $T$. $T$ lines follow. The first line of each test case contains two integers, $N$ denoting the number of vertices and $A$, denoting double the required area of the polygon.

For each test case, output one line containing Case #x: y, where $x$ is the test case number (starting from 1) and $y$ is IMPOSSIBLE if it is not possible to construct a polygon with the given requirements and POSSIBLE otherwise.

If you output POSSIBLE, output $N$ more lines with $2$ integers each. The $i$-th line should contain two integers $X\_i$ and $Y\_i$ which denote the coordinates of the $i$-th vertex. For each $i$, the coordinates should satisfy the $0 \le X\_i,Y\_i ≤ 10^9$ constraints. Vertices of the polygon should be listed in consecutive order ($vertex\_i$ should be adjacent to $vertex\_{i-1}$ and $vertex\_{i+1}$ in the polygon).

If there are multiple possible solutions, you can output any of them.

• $1 \le T \le 100$.
• $1 \le A \le 10^9$.