A robot is on a map that can be viewed as a grid with $N$ rows and $M$ columns. Rows are numbered from $1$ to $N$ from top to bottom while columns are numbered from $1$ to $M$ from left to right. The cell on the $i^{\text{th}}$ row, $j^{\text{th}}$ column is denoted as $(i, j)$. Initially, the robot is located at $(1, 1)$.

To perform movement, it receives a command, which is represented by a string $S$. There are two types of operations:

• Paid Operations (Costs $1$ coin per character appearing in $S$):
• U: The robot moves upwards by $1$ unit, that is, traveling from cell $(X, Y)$ to cell $(X-1, Y)$.
• D: The robot moves downwards by $1$ unit, that is, traveling from cell $(X, Y)$ to cell $(X+1, Y)$.
• L: The robot moves leftwards by $1$ unit, that is, traveling from cell $(X, Y)$ to cell $(X, Y-1)$.
• R: The robot moves rightwards by $1$ unit, that is, traveling from cell $(X, Y)$ to cell $(X, Y+1)$.
• Free operation (Costs $0$ coins):
• (): It repeats the instruction sequence inside the brackets twice. An instruction consists of at least $1$ valid operation or nested instruction.

For example, if $S =$ (RU)(L), the robot executes RURULL. The total cost is $3$ coins. Note that () can be nested. For example, if $S =$ ((D)R), the robot executes DDRDDR, and the total cost is $2$ coins.

However, an earthquake suddenly happens and destroys $K$ rectangular areas of the map! Note that $0 \le K \le 1$. If $K = 0$, nothing happens. Otherwise, if $K = 1$, the broken area is a rectangle with its top-left corner located at $(X_1, Y_1)$ while its bottom-right corner is located at $(X_2, Y_2)$.

More formally, for all pairs of $(i, j)$ such that $X_1 \le i \le X_2$ and $Y_1 \le j \le Y_2$, cell $(i, j)$ becomes broken. It is guaranteed that neither cell $(1, 1)$ nor cell $(N, M)$ is broken.

Your task is to send the robot back home, which is located at $(N, M)$, by constructing $S$. $S$ must satisfy the following rules:

• The length of $S$ must be at most $10^6$. Note that you do not have to minimize the length of $S$.
• $S$ can only contain characters U, D, L, R, ( and ).
• All brackets in $S$ must be well-formed and balanced.
• At any moment, the robot must not go off the map or locate at a broken cell.
• After the command is executed, the robot is located exactly at $(N, M)$.

It is possible that the robot can never go back home. In that case, report -1.

Partial scoring is available for this problem. The fewer coins $S$ uses, the higher score you get. Refer to "Scoring" section for further details.

Input

The first line contains three integers $N, M$ and $K$.

If $K = 1$, the second line contains four integers $X_1$, $Y_1$, $X_2$ and $Y_2$.

Output

If it is not possible to go back home, output -1.

Otherwise, output the string $S$, denoting the command for the robot.

Subtasks

For all test cases:

• $2 \le N, M \le 10^9$
• $0 \le K \le 1$

Subtask	Score	Additional Constraints
$1$	$8$	$N, M \le 100$ $K = 0$
$2$	$19$	$N, M \le 100$
$3$	$56$	$K = 0$
$4$	$17$	No Additional Constraints

Scoring

For a test case, if $S$ violates any of the rules mentioned above, you'll get zero score.

Otherwise, partial scoring will be given for different subtasks.

For subtasks $1$ and $2$, you will receive full score automatically if $S$ is valid.

For subtasks $3$ and $4$, denote the full score of a subtask and the number of coins used in $S$ to be $R$ and $C$ respectively. Your score is calculated according to the following formula:

$$ \text{score} = \begin{cases} R & \text{if } C \le 32 \\ (1 - \frac{3(C-32)}{100})R & \text{if } 32 < C \le 40 \\ (0.76 - \frac{2(C-40)}{100})R & \text{if } 40 < C \le 46 \\ (0.64 - \frac{1.5(C-46)}{100})R & \text{if } 46 < C \le 58 \\ (0.46 - \frac{0.8(C-58)}{100})R & \text{if } 58 < C \le 100 \\ 0 & \text{otherwise.} \end{cases} $$