AT_fps_24_g 硬貨

You have an unlimited number of coins of denominations $ 1 $ , $ 2 $ , $ \dots $ , $ M $ yen. Coins of the same denomination are indistinguishable. You are given integers $ N $ and $ L $ . For each $ m = 1, 2, \dots, M-L+1 $ , solve the following problem: - You may use coins of denominations $ m, m+1, \dots, m+L-1 $ freely. (Formally, you may use coins of denomination $ x $ for all $ x $ satisfying $ m \leq x \leq m+L-1 $ .) Find the number of ways to pay exactly $ N $ yen using these coins, modulo $ 998244353 $ . Two payment methods are considered different if there exists at least one denomination for which the number of coins used differs.

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

Print $ M-L+1 $ lines. On the $ i $ -th line, output the answer for $ m = i $ .

### Sample Explanation 1 For $ m=1 $ , using coins of denominations $ 1 $ and $ 2 $ , there are $ 3 $ ways to pay exactly $ 5 $ yen: - Pay $ 5 $ coins of $ 1 $ yen. - Pay $ 3 $ coins of $ 1 $ yen and $ 1 $ coin of $ 2 $ yen. - Pay $ 1 $ coin of $ 1 $ yen and $ 2 $ coins of $ 2 $ yen. For $ m=2 $ , using coins of denominations $ 2 $ and $ 3 $ , there is $ 1 $ way to pay exactly $ 5 $ yen: - Pay $ 1 $ coin of $ 2 $ yen and $ 1 $ coin of $ 3 $ yen. ### Constraints - $ 1 \leq L \leq M \leq N \leq 5000 $ - $ N, M, L $ are integers