p03054 AtCoder Grand Contest 033 - LRUD Game
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


Output

If the piece will remain on the grid at the end of the game, print `YES`; otherwise, print `NO`.

Examples

Input

2 3 3
2 2
RRL
LUD


Output

YES


Input

4 3 5
2 2
UDRRR
LLDUD


Output

NO


Input

5 6 11
2 1
RLDRRUDDLRL
URRDRLLDLRD


Output

NO
```python
H, W, N = map(int, input().split())
sr, sc = map(int, input().split())
S = input()
T = input()
B = [1, W, 1, H]
for i in range(N - 1, -1, -1):
  if T[i] == 'L': B[1] = min(B[1] + 1, W)
  if T[i] == 'R': B[0] = max(B[0] - 1, 1)
  if T[i] == 'U': B[3] = min(B[3] + 1, H)
  if T[i] == 'D': B[2] = max(B[2] - 1, 1)
  if S[i] == 'L': B[0] += 1
  if S[i] == 'R': B[1] -= 1
  if S[i] == 'U': B[2] += 1
  if S[i] == 'D': B[3] -= 1
  if B[1] < B[0] or B[3] < B[2]:
    print('NO')
    break
else:
  print('YES' if B[0] <= sc <= B[1] and B[2] <= sr <= B[3] else 'NO')
```