{"problem":{"name":"Montage","description":{"content":"You are given positive integers $N$ and $M$. Among the $2^{NM}$ matrices $A$ with $N$ rows and $M$ columns where each element is $0$ or $1$, find the number, modulo $998244353$, of ones that satisfy t","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc162_f"},"statements":[{"statement_type":"Markdown","content":"You are given positive integers $N$ and $M$. Among the $2^{NM}$ matrices $A$ with $N$ rows and $M$ columns where each element is $0$ or $1$, find the number, modulo $998244353$, of ones that satisfy the following condition:\n\n*   $A_{a, b} \\times A_{c, d} \\leq A_{a, d} \\times A_{c, b}$ for every quadruple of integers $(a, b, c, d)$ such that $1 \\leq a < c \\leq N$ and $1 \\leq b < d \\leq M$.\n\n## Constraints\n\n*   $1 \\leq N, M \\leq 400$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc162_f","tags":[],"sample_group":[["2 2","13\n\nThe condition is $A_{1,1} \\times A_{2,2} \\leq A_{1,2} \\times A_{2,1}$. All $13$ matrices other than $\\begin{pmatrix} 1 & 0 \\\\ 0 & 1 \\end{pmatrix}, \\begin{pmatrix} 1 & 1 \\\\ 0 & 1 \\end{pmatrix}, \\begin{pmatrix} 1 & 0 \\\\ 1 & 1 \\end{pmatrix}$ satisfy the condition."],["1 30","75497471\n\nAll $2^{NM}$ matrices satisfy the condition, so print $2^{30}$ modulo $998244353$, that is, $75497471$."],["400 400","412670892"]],"created_at":"2026-03-03 11:01:13"}}