Superfactorial numeral system

On the most perfect of all planets i1c5l various numeral systems are being used during programming contests. In the second division they use a superfactorial numeral system. In this system any positive integer is presented as a linear combination of numbers converse to factorials:

$$\frac{p}{q} = a_1 + \frac{a_2}{2!} + \frac{a_3}{3!} + \ldots + \frac{a_n}{n!}\,.$$

Here $a_1$ is non-negative integer, and integers $a_k$ for $k \ge 2$ satisfy $0 \le a_k < k$. The nonsignificant zeros in the tail of the superfactorial number designation $\frac{p}{q}$ are rejected. The task is to find out how the rational number $\frac{p}{q}$ is presented in the superfactorial numeral system.

Single line contains two space-separated integers $p$ and $q$ ($1 \le p \le 10^6$, $1 \le q \le 10^6$).

Single line should contain a sequence of space-separated integers $a_1, a_2, \ldots, a_n$, forming a number designation $\frac{p}{q}$ in the superfactorial numeral system. If several solution exist, output any of them.