AT_arc232_d [ARC232D] Delete Different

You are given integers $ N $ and $ K $ . For an integer sequence $ S $ consisting of integers between $ 1 $ and $ K $ , inclusive, define its score $ f(S) $ as follows. - Repeat the following operation until all elements of $ S $ are equal. The number of times this operation is performed is $ f(S) $ . - Let $ |S| $ be the length of $ S $ before the operation. For every $ i $ satisfying $ 2 \leq i \leq |S| $ and $ S_{i-1} \ne S_i $ , simultaneously delete the $ i $ -th element of $ S $ . Concatenate the remaining elements in their original order to form the new $ S $ . There are $ K^N $ integer sequences $ S $ of length $ N $ consisting of integers between $ 1 $ and $ K $ , inclusive. Find the sum of $ f(S) $ over all of them, modulo $ 998244353 $ .

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

Output the answer.

### Sample Explanation 1 The scores of $ (1,1,1) $ and $ (2,2,2) $ are $ 0 $ , and the scores of $ (1,2,2) $ and $ (2,1,1) $ are $ 2 $ . The scores of the other four sequences are $ 1 $ , so the sum is $ 8 $ . ### Sample Explanation 2 For example, $ S=(1,2,2,2,1,2) $ changes as follows, so its score is $ 3 $ . $ (1,2,2,2,1,2) \to (1,2,2) \to (1,2) \to (1) $ ### Constraints - $ 2 \leq N \leq 100 $ - $ 2 \leq K < 998244353 $ - All input values are integers.