Another Problem About Dividing Numbers

You are given two integers $$$a$$$ and $$$b$$$. In one turn, you can do one of the following operations:

• Take an integer $$$c$$$ ($$$c > 1$$$ and $$$a$$$ should be divisible by $$$c$$$) and replace $$$a$$$ with $$$\frac{a}{c}$$$;
• Take an integer $$$c$$$ ($$$c > 1$$$ and $$$b$$$ should be divisible by $$$c$$$) and replace $$$b$$$ with $$$\frac{b}{c}$$$.

Your goal is to make $$$a$$$ equal to $$$b$$$ using exactly $$$k$$$ turns.

For example, the numbers $$$a=36$$$ and $$$b=48$$$ can be made equal in $$$4$$$ moves:

• $$$c=6$$$, divide $$$b$$$ by $$$c$$$ $$$\Rightarrow$$$ $$$a=36$$$, $$$b=8$$$;
• $$$c=2$$$, divide $$$a$$$ by $$$c$$$ $$$\Rightarrow$$$ $$$a=18$$$, $$$b=8$$$;
• $$$c=9$$$, divide $$$a$$$ by $$$c$$$ $$$\Rightarrow$$$ $$$a=2$$$, $$$b=8$$$;
• $$$c=4$$$, divide $$$b$$$ by $$$c$$$ $$$\Rightarrow$$$ $$$a=2$$$, $$$b=2$$$.

For the given numbers $$$a$$$ and $$$b$$$, determine whether it is possible to make them equal using exactly $$$k$$$ turns.