{"raw_statement":[{"iden":"problem statement","content":"For $D$ days, each day you choose exactly one of the following four actions:\n\n*   Pay $1$ yen and buy gum.\n*   Pay $3$ yen and buy candy.\n*   Pay $4$ yen and buy chocolate.\n*   Pay $6$ yen and buy wheat gluten snack.\n\nAfter $D$ days, you have paid a total of $N$ yen.  \nHow many possible sequences of $D$ days satisfy this condition? Output the answer modulo $998244353$.\nTwo sequences are considered different if there exists at least one day on which the purchased item is different."},{"iden":"constraints","content":"*   $1 \\leq D \\leq 2 \\times 10^5$\n*   $1 \\leq N \\leq 10^6$\n*   $D, N$ are integers"},{"iden":"input","content":"The input is given from standard input in the following format:\n\n$D$ $N$"},{"iden":"sample input 1","content":"2 7"},{"iden":"sample output 1","content":"4\n\nThere are $4$ valid action sequences for $2$ days:\n\n*   On day $1$, pay $1$ yen for gum; on day $2$, pay $6$ yen for wheat gluten snack.\n*   On day $1$, pay $3$ yen for candy; on day $2$, pay $4$ yen for chocolate.\n*   On day $1$, pay $4$ yen for chocolate; on day $2$, pay $3$ yen for candy.\n*   On day $1$, pay $6$ yen for wheat gluten snack; on day $2$, pay $1$ yen for gum."},{"iden":"sample input 2","content":"200000 1000000"},{"iden":"sample output 2","content":"688682037"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}