{"problem":{"name":"GP 2","description":{"content":"We have a sequence of $N$ integers: $x=(x_0,x_1,\\cdots,x_{N-1})$. Initially, $x_i=0$ for each $i$ ($0 \\leq i \\leq N-1$). Snuke will perform the following operation **exactly** $M$ times: *   Choose t","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc036_c"},"statements":[{"statement_type":"Markdown","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 $998244353$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 10^6$\n*   $1 \\leq M \\leq 5 \\times 10^5$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc036_c","tags":[],"sample_group":[["2 2","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 $(3,3)$."],["3 2","19"],["10 10","211428932"],["100000 50000","3463133"]],"created_at":"2026-03-03 11:01:14"}}