Description:
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.
Input Format:
The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$). Then $$$t$$$ test cases follow.
Each test case is contains three integers $$$a$$$, $$$b$$$ and $$$k$$$ ($$$1 \le a, b, k \le 10^9$$$).
Output Format:
For each test case output:
- "Yes", if it is possible to make the numbers $$$a$$$ and $$$b$$$ equal in exactly $$$k$$$ turns;
- "No" otherwise.
The strings "Yes" and "No" can be output in any case.
Note:
None