CF1472A.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.

为迎接新年，Polycarp 决定向他全部 $n$ 位朋友寄送明信片。他想亲手制作这些明信片。为此，他有一张尺寸为 $w \times h$ 的纸，可以将其裁剪成若干小片。

Polycarp 只能在以下两种情况下，对任意一张他所拥有的尺寸为 $w \times h$ 的纸进行裁剪：

• 若 $w$ 是偶数，则他可将该纸沿宽度方向对半裁开，得到两张尺寸为 $\frac{w}{2} \times h$ 的纸；
• 若 $h$ 是偶数，则他可将该纸沿高度方向对半裁开，得到两张尺寸为 $w \times \frac{h}{2}$ 的纸；

若 $w$ 和 $h$ 同时为偶数，则 Polycarp 可任选上述两种裁剪方式之一执行。

每次裁剪一张纸后，纸的总张数增加 $1$ 张。

请帮助 Polycarp 判断：他能否仅使用上述规则，将一张尺寸为 $w \times h$ 的纸裁剪成至少 $n$ 张？

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.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。接下来是 $t$ 个测试用例。

每个测试用例由一行组成，包含三个整数 $w$、$h$、$n$（$1 \le w, h \le 10^4$，$1 \le n \le 10^9$）—— 分别表示 Polycarp 所拥有的纸张的宽度和高度，以及他需要寄明信片的朋友人数。

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).

对于每个测试用例，在单独的一行上输出：

• 如果可以将一张尺寸为 $w \times h$ 的纸裁剪成至少 $n$ 张，则输出 "YES"；
• 否则输出 "NO"。

你可以以任意大小写形式输出 "YES" 和 "NO"（例如，字符串 yEs、yes、Yes 和 YES 均会被识别为肯定回答）。

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 $1 \times 1$.

在第一个测试用例中，你可以先将 $2 \times 2$ 的纸张裁剪成两张 $2 \times 1$ 的纸张，然后再将每张 $2 \times 1$ 纸张各自裁剪成两张更小的纸张。最终得到四张 $1 \times 1$ 的纸张。我们可以从中任选三张送给朋友。

在第二个测试用例中，$3 \times 3$ 的纸张无法被裁剪，因此不可能得到两张纸张。

在第三个测试用例中，你可以将 $5 \times 10$ 的纸张裁剪成两张 $5 \times 5$ 的纸张。

在第四个测试用例中，无需裁剪纸张，因为我们仅需要一张纸张。

在第五个测试用例中，你可以先将 $1 \times 4$ 的纸张裁剪成两张 $1 \times 2$ 的纸张，然后再将每张 $1 \times 2$ 纸张各自裁剪成两张更小的纸张。最终得到四张 $1 \times 1$ 的纸张。