in c++

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 wh, which can be cut into pieces.

Polycarp can cut any sheet of paper wh 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 w/2h;
• If h is even, then he can cut the sheet in half and get two sheets of size wh/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 wxh at into n or more pieces,using only the rules described above.

Input

The first line contains one integer t (1t104) the number of test cases. Then t test cases follow.

Each test case consists of one line containing three integers w, h, n (1w,h104,1n109) 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 wh 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).

Example

input

Copy

5 2 2 3 3 3 2 5 10 2 11 13 1 1 4 4 

output

YES NO YES YES YES 

Note

In the first test case, you can first cut the 22sheet into two 21 sheets, and then cut each of them into two more sheets. As a result, we get four sheets 11. We can choose any three of them and send them to our friends.

In the second test case, a 33sheet cannot be cut, so it is impossible to get two sheets.

In the third test case, you can cut a 510sheet into two 55 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 14 sheet into two 12sheets, and then cut each of them into two more sheets. As a result, we get four sheets 11