Purify It

*This problem has subtasks.* You are given two integers $L$ and $R$ ($L \leq R$). You want to *purify* each integer in this range. To purify an integer $x$ between $L$ and $R$, you must pay a cost, which is computed as follows: - Choose a positive integer $k$ and some integers $a_1, a_2, \ldots, a_k$ such that: - $L \leq a_i \leq R$ for each $i$. - $\text{lcm}(a_1, a_2, \ldots, a_k) = x