#P1472A. Cards for Friends
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ID: 5740
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Cards for Friends
No submission language available for this problem.
Description
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).
Input
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.
Output
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).
Samples
5
2 2 3
3 3 2
5 10 2
11 13 1
1 4 4
YES
NO
YES
YES
YES
Note
In the first test case, you can first cut the $2 \times 2$ sheet into two $2 \times 1$ sheets, and then cut each of them into two more sheets. As a result, we get four sheets $1 \times 1$. We can choose any three of them and send them to our friends.
In the second test case, a $3 \times 3$ sheet cannot be cut, so it is impossible to get two sheets.
In the third test case, you can cut a $5 \times 10$ sheet into two $5 \times 5$ sheets.
In the fourth test case, there is no need to cut the sheet, since we only need one sheet.
In the fifth test case, you can first cut the $1 \times 4$ sheet into two $1 \times 2$ sheets, and then cut each of them into two more sheets. As a result, we get four sheets $1 \times 1$.