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 × h, which can be cut into pieces.

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

Input

The first line contains one integer t (1 ≤ t ≤ 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 ≤ w, h ≤ 10^4, 1 ≤ n ≤ 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 × 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).

Example

Input

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 2 × 2 sheet into two 2 × 1 sheets, and then cut each of them into two more sheets. As a result, we get four sheets 1 × 1. We can choose any three of them and send them to our friends.

In the second test case, a 3 × 3 sheet cannot be cut, so it is impossible to get two sheets.

In the third test case, you can cut a 5 × 10 sheet into two 5 × 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 × 4 sheet into two 1 × 2 sheets, and then cut each of them into two more sheets. As a result, we get four sheets 1 × 1.

inputFormat

Input

The first line contains one integer t (1 ≤ t ≤ 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 ≤ w, h ≤ 10^4, 1 ≤ n ≤ 10^9) — the width and height of the sheet Polycarp has and the number of friends he needs to send a postcard to.

outputFormat

Output

For each test case, output on a separate line:

• "YES", if it is possible to cut a sheet of size w × 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).

Example

Input

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 2 × 2 sheet into two 2 × 1 sheets, and then cut each of them into two more sheets. As a result, we get four sheets 1 × 1. We can choose any three of them and send them to our friends.

In the second test case, a 3 × 3 sheet cannot be cut, so it is impossible to get two sheets.

In the third test case, you can cut a 5 × 10 sheet into two 5 × 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 × 4 sheet into two 1 × 2 sheets, and then cut each of them into two more sheets. As a result, we get four sheets 1 × 1.

样例

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

YES
NO
YES
YES
YES

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