AT_abc385_g [ABC385G] Counting Buildings

For a permutation $ P=(P_1,P_2,\dots,P_N) $ of $ (1,2,\dots,N) $ , define integers $ L(P) $ and $ R(P) $ as follows: - Consider $ N $ buildings arranged in a row from left to right, with the height of the $ i $ -th building from the left being $ P_i $ . Then $ L(P) $ is the number of buildings visible when viewed from the left, and $ R(P) $ is the number of buildings visible when viewed from the right. More formally, $ L(P) $ is the count of indices $ i $ such that $ P_j < P_i $ for all $ j < i $ , and $ R(P) $ is the count of indices $ i $ such that $ P_i > P_j $ for all $ j > i $ . You are given integers $ N $ and $ K $ . Find, modulo $ 998244353 $ , the count of all permutations $ P $ of $ (1,2,\dots,N) $ such that $ L(P)-R(P)=K $ .

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

Print the answer.

### Sample Explanation 1 - $ P=(1,2,3) $ : $ L(P)-R(P)=3-1=2 $ . - $ P=(1,3,2) $ : $ L(P)-R(P)=2-2=0 $ . - $ P=(2,1,3) $ : $ L(P)-R(P)=2-1=1 $ . - $ P=(2,3,1) $ : $ L(P)-R(P)=2-2=0 $ . - $ P=(3,1,2) $ : $ L(P)-R(P)=1-2=-1 $ . - $ P=(3,2,1) $ : $ L(P)-R(P)=1-3=-2 $ . Therefore, the number of permutations $ P $ with $ L(P)-R(P)=-1 $ is $ 1 $ . ### Sample Explanation 3 Print the count modulo $ 998244353 $ . ### Constraints - $ 1 \leq N \leq 2 \times 10^5 $ - $ |K| \leq N-1 $ - All input values are integers.