A robot is stuck on a infinite two-dimensional grid. Rows are increasing from top to bottom while columns are increasing from left to right. The cell landing on the $i^{th}$ row, $j^{th}$ column is denoted as $(i, j)$.

The robot is initially located at the origin $(0, 0)$. Now, he plans to travel to cell $(X, Y)$ by executing a string command $S$ with length $N$, provided by you. $N$ must be at most $10^5$.

The command $S$ can only have four kinds of characters: U, D, L, R, which represents up, down, left and right respectively.

The robot will first execute the $1^{st}$ character of $S$, then the $2^{nd}$ character, and so on, all the way until the $N^{th}$ character. After that, it will execute the $1^{st}$ character, and the process repeats.

The execution of $1$ character inside $S$ is counted as $1$ operation. After $K$ operations, the robot will end its journey. If currently it lands on cell $(X, Y)$, your mission is considered completed.

Given $X$, $Y$ and $K$, your task is to decide the value of $N$, generate the command $S$, and complete the mission - the robot challenges you. Note that it might be impossible to complete the mission. In this case, report it.

Input

The only line contains three integers $X$, $Y$ and $K$.

Output

If it is impossible to arrive cell $(X, Y)$, output Impossible.

Otherwise, output Possible on the first line.

On the second line, output a single integer $N$ $(1 \le N \le 10^5)$, denoting the length of $S$.

On the third line, output $N$ characters, denoting the command $S$. $S$ must only contain U, D, L, R four characters.

Subtasks

For all test cases:

• $-10^{10} \le X, Y \le 10^{10}$
• $1 \le K \le 10^{10}$