問題文から
\[\begin{array}{c}
A \leq 5000P \lt A+1 \\
B \leq 200000P \lt B+1
\end{array}\]
となる. よって,
\[\begin{array}{c}
A/5000 \leq P \leq (A+1)/5000 \\
B/200000 \leq P \leq (B+1)/200000
\end{array}\]
となり, \(A/5000 \lt (B+1)/200000\) かつ \(B/200000 \lt (A+1)/5000\) であればいい.