The Lost Fraction

Byteasar came up with a really neat fraction whose denominator is at most $n$, but after a while he forgot which fraction it was. He is almost certain that it lay inside the closed interval $\left[\frac{a}{n^2}, \frac{a+1}{n^2}\right]$. Help him by finding every fraction inside this interval whose denominator is at most $n$.

Here a fraction "with denominator at most $n$" means a rational number whose denominator, once the fraction is reduced to lowest terms, is at most $n$. Both endpoints of the interval are included.

The only line contains two integers $n$ and $a$ separated by a single space ($1 \le n < 2^{32}$, $1 \le a < 2^{64}-1$).

On the first line print $m$, the number of distinct reduced fractions that lie in the interval $\left[\frac{a}{n^2}, \frac{a+1}{n^2}\right]$ and have denominator at most $n$.

On each of the following $m$ lines print the numerator and the denominator of one such fraction, separated by a single space. Every fraction must be written in lowest terms, and the fractions must be listed in strictly increasing order of their value.