{"problem":{"name":"Jump","description":{"content":"On a 2D coordinate plane, a piece is placed at $(0, 0)$.   You may perform the following operation any number of times (including zero): *   Choose an integer pair $(a, b)$ such that $0 \\leq a \\leq 1","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"fps_24_h"},"statements":[{"statement_type":"Markdown","content":"On a 2D coordinate plane, a piece is placed at $(0, 0)$.  \nYou may perform the following operation any number of times (including zero):\n\n*   Choose an integer pair $(a, b)$ such that $0 \\leq a \\leq 1$, $0 \\leq b$, and $(a, b) \\neq (0, 0)$.\n*   If the current position of the piece is $(x, y)$, move it to $(x+a, y+b)$.\n\nFind the number of operation sequences that result in the piece being at $(N, M)$ after all operations, and output the answer modulo $998244353$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq M \\leq 2 \\times 10^5$\n*   All input values are integers\n\n## Input\n\nThe input is given from standard input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"fps_24_h","tags":[],"sample_group":[["2 1","5\n\nFor each valid operation sequence, the visited coordinates are as follows (5 possibilities):\n\n*   $(0, 0) \\to (0, 1) \\to (1, 1) \\to (2, 1)$\n*   $(0, 0) \\to (1, 0) \\to (1, 1) \\to (2, 1)$\n*   $(0, 0) \\to (1, 0) \\to (2, 0) \\to (2, 1)$\n*   $(0, 0) \\to (1, 0) \\to (2, 1)$\n*   $(0, 0) \\to (1, 1) \\to (2, 1)$"],["12345 67890","824829859"]],"created_at":"2026-03-03 11:01:14"}}