AT_abc449_g [ABC449G] Many Repunit Sum 2

You are given positive integers $ N, M $ . For a positive integer $ d $ , define the repunit with $ d $ digits as the integer $ \displaystyle\sum_{i = 0}^{d - 1} 10^i $ . Find the number, modulo $ 998244353 $ , of integers that can be expressed as the sum of (not necessarily distinct) $ N $ repunits, each with at least $ 1 $ digit and at most $ M $ digits.

The input is given from Standard Input in the following format: > $ N $ $ M $

Output the answer.

### Sample Explanation 1 We have $ 3 $ repunits with at least $ 1 $ digit and at most $ 3 $ digits: $ 1, 11, 111 $ . As the sum of $ 2 $ of them, we can express $ 6 $ integers: $ 2, 12, 22, 112, 122, 222 $ . ### Constraints - $ 1 \leq N \leq 10^5 $ - $ 1 \leq M \leq 10^9 $ - All input values are integers.