LRUD Game

AtCoder

IDagc033_b

Time2000ms

Memory256MB

Difficulty—

We have a rectangular grid of squares with $H$ horizontal rows and $W$ vertical columns. Let $(i,j)$ denote the square at the $i$\-th row from the top and the $j$\-th column from the left. On this grid, there is a piece, which is initially placed at square $(s_r,s_c)$. Takahashi and Aoki will play a game, where each player has a string of length $N$. Takahashi's string is $S$, and Aoki's string is $T$. $S$ and $T$ both consist of four kinds of letters: `L`, `R`, `U` and `D`. The game consists of $N$ steps. The $i$\-th step proceeds as follows: * First, Takahashi performs a move. He either moves the piece in the direction of $S_i$, or does not move the piece. * Second, Aoki performs a move. He either moves the piece in the direction of $T_i$, or does not move the piece. Here, to move the piece in the direction of `L`, `R`, `U` and `D`, is to move the piece from square $(r,c)$ to square $(r,c-1)$, $(r,c+1)$, $(r-1,c)$ and $(r+1,c)$, respectively. If the destination square does not exist, the piece is removed from the grid, and the game ends, even if less than $N$ steps are done. Takahashi wants to remove the piece from the grid in one of the $N$ steps. Aoki, on the other hand, wants to finish the $N$ steps with the piece remaining on the grid. Determine if the piece will remain on the grid at the end of the game when both players play optimally. ## Constraints * $2 \leq H,W \leq 2 \times 10^5$ * $2 \leq N \leq 2 \times 10^5$ * $1 \leq s_r \leq H$ * $1 \leq s_c \leq W$ * $|S|=|T|=N$ * $S$ and $T$ consists of the four kinds of letters `L`, `R`, `U` and `D`. ## Input Input is given from Standard Input in the following format: $H$ $W$ $N$ $s_r$ $s_c$ $S$ $T$ [samples]

Samples

Input #1

2 3 3
2 2
RRL
LUD

Output #1

YES

Here is one possible progress of the game:

*   Takahashi moves the piece right. The piece is now at $(2,3)$.
*   Aoki moves the piece left. The piece is now at $(2,2)$.
*   Takahashi does not move the piece. The piece remains at $(2,2)$.
*   Aoki moves the piece up. The piece is now at $(1,2)$.
*   Takahashi moves the piece left. The piece is now at $(1,1)$.
*   Aoki does not move the piece. The piece remains at $(1,1)$.

Input #2

4 3 5
2 2
UDRRR
LLDUD

Output #2

NO

Input #3

5 6 11
2 1
RLDRRUDDLRL
URRDRLLDLRD

Output #3

NO

API Response (JSON)

{
  "problem": {
    "name": "LRUD Game",
    "description": {
      "content": "We have a rectangular grid of squares with $H$ horizontal rows and $W$ vertical columns. Let $(i,j)$ denote the square at the $i$\\-th row from the top and the $j$\\-th column from the left. On this gri",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc033_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a rectangular grid of squares with $H$ horizontal rows and $W$ vertical columns. Let $(i,j)$ denote the square at the $i$\\-th row from the top and the $j$\\-th column from the left. On this gri...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments