1538D · Another Problem About Dividing Numbers

Problem: 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.