AtCoder Regular Contest 162
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Problem Statement
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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:
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$A_{a, b} \times A_{c, d} \leq A_{a, d} \times A_{c, b}$for every quadruple of integers$(a, b, c, d)$such that$1 \leq a < c \leq N$and$1 \leq b < d \leq M$.
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Constraints
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$1 \leq N, M \leq 400$- All input values are integers.
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Input
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The input is given from Standard Input in the following format:
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N M翻译中…
Output
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Print the answer in a single line.
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样例
Input #1
2 2
Output #1
13
The 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.
Input #2
1 30
Output #2
75497471
All $2^{NM}$ matrices satisfy the condition, so print $2^{30}$ modulo $998244353$, that is, $75497471$.
Input #3
400 400
Output #3
412670892
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。