Path Through Graph

Problem Description

You are given two natural numbers. Imagine these natural numbers as nodes on a graph. On this graph, a number is connected to its largest factor other than itself. You have to find the shortest path between them and print the number of edges on that path.
If the two numbers do not have any common factor, then construct a path through 1. For better understanding refer to the examples below:

Example 1:

 Input numbers: 2 4

The numbers are directly connected as follows on the graph. 2 is the largest factor of 4, other than itself. We can also see that there is only on edge between them.

4 <–> 2

Hence the number of edges in shortest path is 1.



Example 2:

 Input numbers: 18 19

The graph for number 18 and 19 will look like this. Here we have 4 edges in the path.

18 <–> 9 <–> 3 <–> 1 <–> 19



Example 3:

Input numbers: 9 9

The number of edges in shortest path is zero since the numbers correspond to the same node.