{"problem":{"name":"Chance Meeting","description":{"content":"Given is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left. Initially, a camel is on $(1, 1)$, and a cat is on $(H, ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc124_f"},"statements":[{"statement_type":"Markdown","content":"Given is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left.\nInitially, a camel is on $(1, 1)$, and a cat is on $(H, 1)$.\nYou can send the following four kinds of orders.\n\n*   `R`: Move the camel on $(i, j)$ to $(i, j+1)$.\n*   `D`: Move the camel on $(i, j)$ to $(i+1, j)$.\n*   `r`: Move the cat on $(i, j)$ to $(i, j+1)$.\n*   `u`: Move the cat on $(i, j)$ to $(i-1, j)$.\n\nA sequence of orders satisfying all of the four conditions below is said to be **good**. Find the number of good sequences of orders, modulo $998244353$.\n\n1.  The final position of the camel will be $(H, W)$.\n2.  The final position of the cat will be $(1, W)$.\n3.  The following will happen exactly once: the camel and the cat are on the same square after an order is processed.\n4.  Neither the camel nor the cat will leave the grid.\n\n## Constraints\n\n*   All values in input are integers.\n*   $2 \\leq H,W \\leq 2 \\times 10^{5}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$H$ $W$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc124_f","tags":[],"sample_group":[["2 2","16\n\n*   The good sequences of orders include `DRur`, `DurR`, `RruD`, `RDru`, but not `DRru`, `RRR`."],["200000 200000","412709667\n\n*   Be sure to print the count modulo $998244353$."]],"created_at":"2026-03-03 11:01:14"}}