A14008 | Cards for Friends

For the New Year, Polycarp decided to send postcards to all his $n$ friends. He wants to make postcards with his own hands. For this purpose, he has a sheet of paper of size $w \times h$ , which can be cut into pieces.

Polycarp can cut any sheet of paper $w \times h$ that he has in only two cases:

- If $w$ is even, then he can cut the sheet in half and get two sheets of size $\frac{w}{2} \times h$ ;
- If $h$ is even, then he can cut the sheet in half and get two sheets of size $w \times \frac{h}{2}$ ;

If $w$ and $h$ are even at the same time, then Polycarp can cut the sheet according to any of the rules above.

After cutting a sheet of paper, the total number of sheets of paper is increased by $1$ .

Help Polycarp to find out if he can cut his sheet of size $w \times h$ at into $n$ or more pieces, using only the rules described above.

The first line contains one integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. Then $t$ test cases follow.

Each test case consists of one line containing three integers $w$ , $h$ , $n$ ( $1 \le w, h \le 10^4, 1 \le n \le 10^9$ ) — the width and height of the sheet Polycarp has and the number of friends he needs to send a postcard to.

For each test case, output on a separate line:

- "YES", if it is possible to cut a sheet of size $w \times h$ into at least $n$ pieces;
- "NO" otherwise.

You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).