{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $2 \\leq H,W \\leq 2 \\times 10^{5}$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$H$ $W$"},{"iden":"sample input 1","content":"2 2"},{"iden":"sample output 1","content":"16\n\n*   The good sequences of orders include `DRur`, `DurR`, `RruD`, `RDru`, but not `DRru`, `RRR`."},{"iden":"sample input 2","content":"200000 200000"},{"iden":"sample output 2","content":"412709667\n\n*   Be sure to print the count modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}