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C - Belt Conveyor

Score : $300$ points

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.

Constraints

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

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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.

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2 3
RDU
LRU

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 $(1, 3)$.

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2 3
RRD
ULL

-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.

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9 44
RRDDDDRRRDDDRRRRRRDDDRDDDDRDDRDDDDDDRRDRRRRR
RRRDLRDRDLLLLRDRRLLLDDRDLLLRDDDLLLDRRLLLLLDD
DRDLRLDRDLRDRLDRLRDDLDDLRDRLDRLDDRLRRLRRRDRR
DDLRRDLDDLDDRLDDLDRDDRDDDDRLRRLRDDRRRLDRDRDD
RDLRRDLRDLLLLRRDLRDRRDRRRDLRDDLLLLDDDLLLLRDR
RDLLLLLRDLRDRLDDLDDRDRRDRLDRRRLDDDLDDDRDDLDR
RDLRRDLDDLRDRLRDLDDDLDDRLDRDRDLDRDLDDLRRDLRR
RDLDRRLDRLLLLDRDRLLLRDDLLLLLRDRLLLRRRRLLLDDR
RRRRDRDDRRRDDRDDDRRRDRDRDRDRRRRRRDDDRDDDDRRR

9 5