AT_fps_24_p ボール

You are given integers $ N, M, K $ . For each $ m = 1, 2, \dots, M $ , solve the following problem: > There are $ N $ balls numbered $ 1 $ through $ N $ , and $ m+1 $ boxes numbered $ 0 $ through $ m $ . > Box $ 0 $ can hold at most $ K $ balls. The other boxes have no upper limit. > Find the number of ways to place all $ N $ balls into the boxes, modulo $ 998244353 $ . > Two placements are considered different if there exists at least one ball that is placed in different boxes between the two placements.

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

Print $ M $ lines. On the $ i $ -th line, output the answer for $ m = i $ .

### Sample Explanation 1 Consider the case $ m=1 $ . There are $ 4 $ valid placements of the balls: - Put balls $ 1,2,3 $ into box $ 1 $ . - Put ball $ 1 $ into box $ 0 $ , and balls $ 2,3 $ into box $ 1 $ . - Put ball $ 2 $ into box $ 0 $ , and balls $ 1,3 $ into box $ 1 $ . - Put ball $ 3 $ into box $ 0 $ , and balls $ 1,2 $ into box $ 1 $ . ### Constraints - $ 1 \leq N \leq 10^5 $ - $ 1 \leq M \leq 10^5 $ - $ 1 \leq K \leq N $ - All input values are integers