Teaching Hazard

Teaching students is fun, but it can turn embarrassing, and that is what happened to me a few days ago. It was the first meeting of a university course, so I was covering something very basic: how to count the zeroes at the end of $n!$ written in base $b$. The number of times a prime $p$ divides $n!$ is

$\left\lfloor \frac{n}{p} \right\rfloor + \left\lfloor \frac{n}{p^2} \right\rfloor + \left\lfloor \frac{n}{p^3} \right\rfloor + \cdots$

and the same formula, used carefully, gives the number of zeroes at the end of $n!$.

After explaining it I worked out the number of trailing zeroes of $200!$ in decimal, then asked with an evil smile for the number of trailing zeroes of $100!$ in hexadecimal. I already knew the answer is 24. To my surprise a student replied 24 within minutes, so I congratulated him. A minute later I checked his script and found that he had counted the trailing zeroes of $100!$ in decimal instead of hexadecimal, and both answers happened to be 24. I was a bit embarrassed, and now I want to know why the two answers agreed.

For an integer $b \ge 2$, let $Z(n, b)$ be the number of zeroes that run backwards from the last digit of $n!$ written in base $b$. Given $n$ and $x$, count the pairs $(b_1, b_2)$ with $2 \le b_1 < b_2$ such that $Z(n, b_1) = Z(n, b_2) = p$ for some integer $p \ge x$.

The input has several lines. Each line contains two integers $n$ ($1 \le n \le 100000$) and $x$ ($2 \le x \le 2500$), separated by a space. The last line contains two zeroes and is not processed. Excluding that line, the input has at most 1000 lines.

For each line of input print the number of pairs $(b_1, b_2)$ on its own line. Every input is such that no output value exceeds $5 \times 10^{18}$.