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.