Maija is playing with a weird chess board. She is trying to find a way to tour all the squares on the board by moving a pawn up, down, left or right. The pawn should visit each square exactly once. The board is $n$ squares tall and $m$ squares wide. The board's upper left corner has coordinates $(1, 1)$ and the lower right corner is at $(n, m)$. Find a sequence of moves that starts and ends in $(1, 1)$ and visits all the squares or report that no such sequence exists.

Input

A single line contains two integer $n$ and $m$.

Output

Print a string of length $n \times m$ that describes the tour: the $i$-th letter is "L" if the $i$-th move is left. "R" corresponds to right, "U" to up and "D" to down. Otherwise, print "-1" if there are no suitable sequences.

Constraints

• $2 \leq n, m \leq 1000$

Example 1

Input:

4 2

Output:

DDDRUUUL

Example 2

Input:

3 3

Output:

-1