Continued fraction#256
A continued fraction is an expression of the form:
In this expression, a_0 is an integer, and the other a_n are positive integers. Continued fractions are interesting because they can represent any real number. For rational numbers, a continued fraction is finite, while for irrational numbers it is infinite.
For example, the number can be represented as a continued fraction: 9/4 = 2 + 1/(3+1/1).
This fraction can also be expressed as: 9/4 = 2 + 1/4.
Your task is to find the minimal continued fraction representation for a given rational number .
The first line of the input contains two integers and (1 \leq p,\ q \leq 10^3).
On the first line of the output, print the number , which is the number of terms in the continued fraction equal to . On the second line, print the numbers a_0, a_1, \ldots, a_n separated by spaces.
Example 1