{"raw_statement":[{"iden":"problem statement","content":"Find the number of permutations $P=(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$ that satisfy the following, modulo $998244353$, for each $K=0,1,2,\\dots,N-1$.\n\n*   There are exactly $K$ integers $i$ such that $1 \\le i \\le N-1$ and $|P_i - P_{i+1}|=M$."},{"iden":"constraints","content":"*   $2 \\le N \\le 250000$\n*   $1 \\le M \\le N-1$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"3 1"},{"iden":"sample output 1","content":"0 4 2 \n\n*   For $K=0$, the condition is satisfied by no permutations $P$.\n*   For $K=1$, the condition is satisfied by four permutations $P$: $(1,3,2),(2,1,3),(2,3,1),(3,1,2)$.\n*   For $K=2$, the condition is satisfied by two permutations $P$: $(1,2,3),(3,2,1)$."},{"iden":"sample input 2","content":"4 3"},{"iden":"sample output 2","content":"12 12 0 0"},{"iden":"sample input 3","content":"10 5"},{"iden":"sample output 3","content":"1263360 1401600 710400 211200 38400 3840 0 0 0 0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}