Factorial Factors

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

For example, \begin{align\*} s(1) &= 1,\\\ s(2) &= 2,\quad \text{(because $1!$ (=1) is not divisible by 2, but $2!$ (=2) is)}\\\ s(4) &= 4,\quad \text{($3!$ (=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 $A$ and $B$, to find the sum:

$s(A) + s(A+1) + \ldots + s(B).$

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

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