{"raw_statement":[{"iden":"problem statement","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 $998244353$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq M \\leq 2 \\times 10^5$\n*   All input values are integers"},{"iden":"input","content":"The input is given from standard input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"2 1"},{"iden":"sample output 1","content":"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*   $(0, 0) \\to (1, 1) \\to (2, 1)$"},{"iden":"sample input 2","content":"12345 67890"},{"iden":"sample output 2","content":"824829859"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}