CF1989E Distance to Different

Consider an array $ a $ of $ n $ integers, where every element is from $ 1 $ to $ k $ , and every integer from $ 1 $ to $ k $ appears at least once. Let the array $ b $ be constructed as follows: for the $ i $ -th element of $ a $ , $ b_i $ is the distance to the closest element in $ a $ which is not equal to $ a_i $ . In other words, $ b_i = \min \limits_{j \in [1, n], a_j \ne a_i} |i - j| $ . For example, if $ a = [1, 1, 2, 3, 3, 3, 3, 1] $ , then $ b = [2, 1, 1, 1, 2, 2, 1, 1] $ . Calculate the number of different arrays $ b $ you can obtain if you consider all possible arrays $ a $ , and print it modulo $ 998244353 $ .

The only line of the input contains two integers $ n $ and $ k $ ( $ 2 \le n \le 2 \cdot 10^5 $ ; $ 2 \le k \le \min(n, 10) $ ).

Print one integer — the number of different arrays $ b $ you can obtain, taken modulo $ 998244353 $ .