Catalina needs help with her Math homework, which consists of finding all the increasing arithmetic progressions of integers (*) that meet the following conditions:

• The progression contains the number $A$
• The sum of the terms of the progression is $S$
• All terms of the progression are in the range $[L, R]$

Catalina is a responsible girl and doesn't want someone else to solve the task for her, but she could use a little help. What Catalina needs is for you to tell her how many progressions exist under these conditions, so that she could know when to stop searching.

(*) An increasing arithmetic progression of integers is a non-empty list of $n$ integer numbers $x_1, x_2, \ldots , x_n$ where $x_i - x_{i-1} = D > 0$ for every integer $i$ such that $2 \leq i \leq n$, where $D$ is a positive integer. For example, $[7]$, $[1, 2, 3]$ and $[2, 4, 6, 8]$ are valid progressions, but $[5, 1]$, $[2, 4, 8]$ and $[3, 6, 9, 6]$ are not.