{"raw_statement":[{"iden":"problem statement","content":"There is a grid with $N$ rows and $N$ columns. Let $(i, j)$ denote the cell at the $i$\\-th row from the top and the $j$\\-th column from the left. Additionally, there is one black stone and $M$ white stones.  \nYou will play a single-player game using these items.\nHere are the rules. Initially, you place the black stone at $(A, B)$. Then, you place each of the $M$ white stones on some cell of the grid. Here:\n\n*   You cannot place a white stone at $(A, B)$.\n*   You can place at most one white stone per row.\n*   You can place at most one white stone per column.\n\nThen, you will perform the following operation until you cannot do so:\n\n*   Assume the black stone is at $(i, j)$. Perform one of the four operations below:\n    *   If there is a white stone at $(i, k)$ where $(j < k)$, remove that white stone and move the black stone to $(i, k + 1)$.\n    *   If there is a white stone at $(i, k)$ where $(j > k)$, remove that white stone and move the black stone to $(i, k - 1)$.\n    *   If there is a white stone at $(k, j)$ where $(i < k)$, remove that white stone and move the black stone to $(k + 1, j)$.\n    *   If there is a white stone at $(k, j)$ where $(i > k)$, remove that white stone and move the black stone to $(k - 1, j)$.\n        *   Here, if the cell to which the black stone is to be moved does not exist, such a move cannot be made.\n\nThe following figure illustrates an example. Here, `B` represents the black stone, `W` represents a white stone, `.` represents an empty cell, and `O` represents a cell to which the black stone can be moved.\n\n..O...\n..W...\n......\n......\n..B.WO\n......\n\nYou win the game if all of the following conditions are satisfied when you finish performing the operation. Otherwise, you lose.\n\n*   All white stones have been removed from the grid.\n*   The black stone is placed at $(A, B)$.\n\nIn how many initial configurations of the $M$ white stones can you win the game by optimally performing the operation? Find the count modulo $998244353$."},{"iden":"constraints","content":"*   $2 \\leq M \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq A \\leq N$\n*   $1 \\leq B \\leq N$\n*   $N$, $M$, $A$, and $B$ are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$ $A$ $B$"},{"iden":"sample input 1","content":"6 4 2 3"},{"iden":"sample output 1","content":"4\n\nFor example, consider the white stones placed as shown in the following figure:\n\n......\n..BW..\n.....W\n......\n..W...\n....W.\n\nHere, you can win the game by moving the black stone in the following steps:\n\n*   Remove the white stone at $(5, 3)$ and move the black stone to $(6, 3)$.\n*   Remove the white stone at $(6, 5)$ and move the black stone to $(6, 6)$.\n*   Remove the white stone at $(3, 6)$ and move the black stone to $(2, 6)$.\n*   Remove the white stone at $(2, 4)$ and move the black stone to $(2, 3)$.\n*   Since all white stones have been removed from the grid and the black stone is placed at $(A, B) = (2, 3)$, you win the game.\n\nThere are four configurations of white stones that can lead to your victory."},{"iden":"sample input 2","content":"5 3 1 3"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"200000 47718 21994 98917"},{"iden":"sample output 3","content":"146958602"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}