402064: GYM100637 J 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.

1 2

0 1 

2 10

0 0 1 0 4 

10 2

5