{"raw_statement":[{"iden":"problem statement","content":"Find the number, modulo $998244353$, of non-decreasing sequences $A=(A_1,A_2,\\ldots,A_N)$ of length $N$ consisting of integers between $0$ and $M$ (inclusive) that satisfy the following, for each $K=0,1,\\ldots,\\mathrm{MOD}-1$:\n\n*   the sum of the elements in $A$ is congruent to $K$ modulo $\\mathrm{MOD}$.\n\nWhat is a non-decreasing sequence? A sequence $B$ is non-decreasing if and only if $B_i \\leq B_{i+1}$ for every integer ($1 \\le i \\le |B| - 1$), where $|B|$ is the length of $B$."},{"iden":"constraints","content":"*   $1 \\leq N ,M\\leq 10^6$\n*   $1\\leq \\mathrm{MOD}\\leq 500$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$ $\\mathrm{MOD}$"},{"iden":"sample input 1","content":"2 2 4"},{"iden":"sample output 1","content":"2 1 2 1\n\nThere are $6$ non-decreasing sequences of length $2$ consisting of integers between $0$ and $2$: $(0, 0), (0, 1),(0,2), (1,1),(1,2),(2,2)$. Here, we have:\n\n*   $2$ sequences whose sums are congruent to $0$ modulo $4$: $(0,0),(2,2)$;\n    \n*   $1$ sequence whose sum is congruent to $1$ modulo $4$: $(0,1)$;\n    \n*   $2$ sequences whose sums are congruent to $2$ modulo $4$: $(0,2),(1,1)$;\n    \n*   $1$ sequence whose sum is congruent to $3$ modulo $4$: $(1,2)$."},{"iden":"sample input 2","content":"3 45 3"},{"iden":"sample output 2","content":"5776 5760 5760"},{"iden":"sample input 3","content":"1000000 1000000 6"},{"iden":"sample output 3","content":"340418986 783857865 191848859 783857865 340418986 635287738\n\nPrint the counts modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}