AT_fps_24_a お菓子

For $ D $ days, each day you choose exactly one of the following four actions: - Pay $ 1 $ yen and buy gum. - Pay $ 3 $ yen and buy candy. - Pay $ 4 $ yen and buy chocolate. - Pay $ 6 $ yen and buy wheat gluten snack. After $ D $ days, you have paid a total of $ N $ yen. How many possible sequences of $ D $ days satisfy this condition? Output the answer modulo $ 998244353 $ . Two sequences are considered different if there exists at least one day on which the purchased item is different.

The input is given from standard input in the following format: > $ D $ $ N $

Print the answer.

### Sample Explanation 1 There are $ 4 $ valid action sequences for $ 2 $ days: - On day $ 1 $ , pay $ 1 $ yen for gum; on day $ 2 $ , pay $ 6 $ yen for wheat gluten snack. - On day $ 1 $ , pay $ 3 $ yen for candy; on day $ 2 $ , pay $ 4 $ yen for chocolate. - On day $ 1 $ , pay $ 4 $ yen for chocolate; on day $ 2 $ , pay $ 3 $ yen for candy. - On day $ 1 $ , pay $ 6 $ yen for wheat gluten snack; on day $ 2 $ , pay $ 1 $ yen for gum. ### Constraints - $ 1 \leq D \leq 2 \times 10^5 $ - $ 1 \leq N \leq 10^6 $ - $ D, N $ are integers