### Writing a given permutaion as a product of generators

Suppose that I have a group generated by three elements (written in cycle notation). I know that Sage will find all of the elements of this group.

What I need is to be able to write a given permutation as a product of these generators.

Any ideas?

For refernce, I am working in S_16. My generators are a=(13,14,15,16), b=(1,2,3,4)(5,6,7,8)(9,10,11,12), and c=(1,5,9,13,12,8,4). I want to "factor" (1,2) and (1,5) as a product of a,b,c.