{"problem":{"name":"Extension","description":{"content":"We have a grid with $A$ horizontal rows and $B$ vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation: *   Assume that the grid currently ha","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc046_b"},"statements":[{"statement_type":"Markdown","content":"We have a grid with $A$ horizontal rows and $B$ vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation:\n\n*   Assume that the grid currently has $a$ horizontal rows and $b$ vertical columns. Choose \"vertical\" or \"horizontal\".\n    *   If we choose \"vertical\", insert one row at the top of the grid, resulting in an $(a+1) \\times b$ grid.\n    *   If we choose \"horizontal\", insert one column at the right end of the grid, resulting in an $a \\times (b+1)$ grid.\n*   Then, paint one of the added squares black, and the other squares white.\n\nAssume the grid eventually has $C$ horizontal rows and $D$ vertical columns. Find the number of ways in which the squares can be painted in the end, modulo $998244353$.\n\n## Constraints\n\n*   $1 \\leq A \\leq C \\leq 3000$\n*   $1 \\leq B \\leq D \\leq 3000$\n*   $A$, $B$, $C$, and $D$ are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$A$ $B$ $C$ $D$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc046_b","tags":[],"sample_group":[["1 1 2 2","3\n\nAny two of the three squares other than the bottom-left square can be painted black."],["2 1 3 4","65"],["31 41 59 265","387222020"]],"created_at":"2026-03-03 11:01:14"}}