The Slivians are afraid of factoring; it's just, well, difficult. Really, they don't even care about the factors themselves, just how much they sum to. We can define $F(n)$ as the sum of all of the factors of $n$; so $F(6) = 12$ and $F(12) = 28$. Your task is, given two integers $a$ and $b$ with $a \le b$, to calculate $$ S=\sum\limits_{a\le n\le b}F(n). $$

The input consists of a single line containing space-separated integers $a$ and $b$ $(1 \le a \le b \le 10^{12};\ b - a \le 10^6)$.

Print $S$ on a single line.

2017 Pacific Northwest Region Programming Contest