{"raw_statement":[{"iden":"problem statement","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 grid, there is a piece, which is initially placed at square $(s_r,s_c)$.\nTakahashi 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`.\nThe game consists of $N$ steps. The $i$\\-th step proceeds as follows:\n\n*   First, Takahashi performs a move. He either moves the piece in the direction of $S_i$, or does not move the piece.\n*   Second, Aoki performs a move. He either moves the piece in the direction of $T_i$, or does not move the piece.\n\nHere, 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.\nTakahashi 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."},{"iden":"constraints","content":"*   $2 \\leq H,W \\leq 2 \\times 10^5$\n*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq s_r \\leq H$\n*   $1 \\leq s_c \\leq W$\n*   $|S|=|T|=N$\n*   $S$ and $T$ consists of the four kinds of letters `L`, `R`, `U` and `D`."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$H$ $W$ $N$\n$s_r$ $s_c$\n$S$\n$T$"},{"iden":"sample input 1","content":"2 3 3\n2 2\nRRL\nLUD"},{"iden":"sample output 1","content":"YES\n\nHere is one possible progress of the game:\n\n*   Takahashi moves the piece right. The piece is now at $(2,3)$.\n*   Aoki moves the piece left. The piece is now at $(2,2)$.\n*   Takahashi does not move the piece. The piece remains at $(2,2)$.\n*   Aoki moves the piece up. The piece is now at $(1,2)$.\n*   Takahashi moves the piece left. The piece is now at $(1,1)$.\n*   Aoki does not move the piece. The piece remains at $(1,1)$."},{"iden":"sample input 2","content":"4 3 5\n2 2\nUDRRR\nLLDUD"},{"iden":"sample output 2","content":"NO"},{"iden":"sample input 3","content":"5 6 11\n2 1\nRLDRRUDDLRL\nURRDRLLDLRD"},{"iden":"sample output 3","content":"NO"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}