D. Another Problem About Dividing Numbers
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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

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.

Example
Input
8
36 48 2
36 48 3
36 48 4
2 8 1
2 8 2
1000000000 1000000000 1000000000
1 2 1
2 2 1
Output
YES
YES
YES
YES
YES
NO
YES
NO