CF 105164H - Highest Score APPQ

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Solve time: 42s
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Solution

Problem Understanding

We are given a universe of numbers generated in a very structured way. Each number corresponds to a vector of exponents over the first $n$ primes. The $i$-th coordinate $e_i$ tells us how many times the $i$-th prime appears in the factorization, and each coordinate is bounded by $0 \le e_i \le a_i$. So the entire input describes a finite grid of exponent vectors, and every valid number is one point in this grid.

We must choose a subset of these numbers under a structural restriction on pairs. If we take two numbers $x < y$, then it is forbidden tha