Factorial Factors

문제

For any positive integer $nn$, define $s(n)s(n)$ as the smallest positive integer $mm$, whose factorial\footnote{The factorial of a positive integer $mm$ (denoted as $m!m!$) is the product of all integers from 1 to $mm$: $$m!:=1\cdot 2\cdot 3\cdot \dots \cdot m\mathrm{.}m!\; :=\; 1\backslash cdot\; 2\; \backslash cdot\; 3\; \backslash cdot\; \backslash ldots\; \backslash cdot\; m.$$ is divisible by $nn$.

For example, $\begin{align*} s(1) &= 1,\\ s(2) &= 2,\quad \text{(because 1!$(=1)isnotdivisibleby2,but(=1)\; is\; not\; divisible\; by\; 2,\; but$2! (=2) is)}\\ s(4) &= 4,\quad \text{(3!$(=6)isnotdivisibleby4,but(=6)\; is\; not\; divisible\; by\; 4,\; but$4! (=24) is)}\\ s(6) &= 3,\quad \text{(3! (=6) is divisible by 6)}\\ s(9) &= 6,\quad \text{(6! (=720) is divisible by 9)}\\ s(10) &= 5,\quad \text{etc}\\ \end{align*}$

The task is, given two integers $AA$ and $BB$, to find the sum:

$$s(A)+s(A+1)+\dots +s(B)\mathrm{.}s(A)\; +\; s(A+1)\; +\; \backslash ldots\; +\; s(B).$$

입력

The single line of input contains two space-separated integers: $AA$ and $BB$ ($1\le A\le B\le 10000001\; \backslash le\; A\; \backslash le\; B\; \backslash le\; 1\backslash ,000\backslash ,000$).

출력

The first and only line of output should contain the required sum.