{"raw_statement":[{"iden":"problem statement","content":"We have a sequence of $N$ integers: $x=(x_0,x_1,\\cdots,x_{N-1})$. Initially, $x_i=0$ for each $i$ ($0 \\leq i \\leq N-1$).\nSnuke will perform the following operation **exactly** $M$ times:\n\n*   Choose two distinct indices $i, j$ ($0 \\leq i,j \\leq N-1,\\ i \\neq j$). Then, replace $x_i$ with $x_i+2$ and $x_j$ with $x_j+1$.\n\nFind the number of different sequences that can result after $M$ operations. Since it can be enormous, compute the count modulo $998244353$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 10^6$\n*   $1 \\leq M \\leq 5 \\times 10^5$\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":"2 2"},{"iden":"sample output 1","content":"3\n\nAfter two operations, there are three possible outcomes:\n\n*   $x=(2,4)$\n*   $x=(3,3)$\n*   $x=(4,2)$\n\nFor example, $x=(3,3)$ can result after the following sequence of operations:\n\n*   First, choose $i=0,j=1$, changing $x$ from $(0,0)$ to $(2,1)$.\n*   Second, choose $i=1,j=0$, changing $x$ from $(2,1)$ to $(3,3)$."},{"iden":"sample input 2","content":"3 2"},{"iden":"sample output 2","content":"19"},{"iden":"sample input 3","content":"10 10"},{"iden":"sample output 3","content":"211428932"},{"iden":"sample input 4","content":"100000 50000"},{"iden":"sample output 4","content":"3463133"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}