Problem Statement

We have a grid with H horizontal rows and W vertical columns. (i, j) denotes the square at the i-th row from the top and j-th column from the left.
(i,j) has a character G_{i,j} written on it. G_{i,j} is U, D, L, or R.
You are initially at (1,1). You repeat the following operation until you cannot make a move.

Let (i,j) be the square you are currently at.
If G_{i,j} is U and $i \neq 1,$ move to (i-1,j).
If G_{i,j} is D and $i \neq H,$ move to (i+1,j).
If G_{i,j} is L and $j \neq 1,$ move to (i,j-1).
If G_{i,j} is R and $j \neq W,$ move to (i,j+1).
Otherwise, you cannot make a move.

Print the square you end up at when you cannot make a move.
If you indefinitely repeat moving, print -1 instead.

Input

Input is given from Standard Input in the following format:
H W
$G_{1,1}G_{1,2}\dots G_{1,W}$
$G_{2,1}G_{2,2}\dots G_{2,W}$
$\vdots$
$G_{H,1}G_{H,2}\dots G_{H,W}$

Output

If you end up at (i, j), print it in the following format:
i j

If you indefinitely repeat moving, print -1.

Constraints

• $1 \leq H, W \leq 500$
• G_{i,j} is U, D, L, or R.
• H and W are integers.

Sample Input 1

2 3
RDU
LRU

Sample Output 1

1 3

You will move as $(1, 1) \to$ $(1, 2) \to$ $(2, 2) \to$ $(2, 3) \to$ (1, 3), ending up here, so the answer is (1, 3).

Sample Input 2

2 3
RRD
ULL

Sample Output 2

-1

You will indefinitely repeat moving as $(1, 1) \to$ $(1, 2) \to$ $(1, 3) \to$ $(2, 3) \to$ $(2, 2) \to$ $(2, 1) \to$ $(1, 1) \to$ $(1, 2) \to$ $\dots$, so -1 should be printed in this case.

Sample Input 3

9 44
RRDDDDRRRDDDRRRRRRDDDRDDDDRDDRDDDDDDRRDRRRRR
RRRDLRDRDLLLLRDRRLLLDDRDLLLRDDDLLLDRRLLLLLDD
DRDLRLDRDLRDRLDRLRDDLDDLRDRLDRLDDRLRRLRRRDRR
DDLRRDLDDLDDRLDDLDRDDRDDDDRLRRLRDDRRRLDRDRDD
RDLRRDLRDLLLLRRDLRDRRDRRRDLRDDLLLLDDDLLLLRDR
RDLLLLLRDLRDRLDDLDDRDRRDRLDRRRLDDDLDDDRDDLDR
RDLRRDLDDLRDRLRDLDDDLDDRLDRDRDLDRDLDDLRRDLRR
RDLDRRLDRLLLLDRDRLLLRDDLLLLLRDRLLLRRRRLLLDDR
RRRRDRDDRRRDDRDDDRRRDRDRDRDRRRRRRDDDRDDDDRRR

Sample Output 3

9 5

见题面 Input 部分

见题面 Output 部分