P8636 [Lanquiao Cup 2016 NOI Qualifier AB] Maximum Ratio.

A Grand Prix on Planet X offers $M$ levels of prizes. The prize money at each level is a positive integer. Moreover, the ratio between two adjacent levels is a fixed value. That is, the prize amounts for all levels form a geometric sequence. For example: $$16,24,36,54$$ Its common ratio is $3/2$. Now, we randomly surveyed the prize amounts of some winners. Based on this, please infer the maximum possible common ratio.

The first line contains an integer $N(0

Output a fraction in the form $A/B$, where $A$ and $B$ are coprime, representing the maximum possible ratio coefficient. The testdata guarantees that the input format is correct, and that the maximum ratio exists.

Time limit: 3 seconds, 256M. The 7th Lanqiao Cup provincial contest in 2016. Lanqiao Cup 2016 provincial contest Group A Problem J (Group B Problem J). Translated by ChatGPT 5