Cards for Friends

题意翻译

### 题目描述 为了庆祝新年，Ploycarp 计划给他所有 $n$ 个朋友寄送明信片。他想要亲手制作。为了这个目标，他准备了一张 $w\times h$ 的纸，他可将其剪成若干片。 Polycarp 可以剪开任意一张其所拥有的形如 $w\times h$ 的纸按照以下两种方式： - 如果 $w$ 是偶数，那么他可以将该纸片对半剪开，得到两张 $\frac{w}{2}\times h$ 的纸片； - 如果 $h$ 是偶数，那么他可以将该纸片对半剪开，得到两张 $w\times \frac{h}{2}$ 的纸片； 如果 $w$ 和 $h$ 同为偶数，那么 Polycarp 可以以任意一种方式将这张纸片剪开。 经过对纸张的裁剪，纸张的总数从 $1$ 开始逐渐增加。 请帮助 Polycarp 找出他是否可以在仅仅使用以上两种方式的情况下，把纸张剪出 $n$ 张或更多。 ### 输入格式 第一行一个整数 $t$（$1\le t\le 10^4$），表示数据组数。 接下来的 $t$ 行，每行三个整数 $w,h,n$（$1\le w,h\le 10^4,1\le n\le 10^9$），意义如题目描述。 ### 输出格式 输出共 $t$ 行，对于魅族数据，输出一行一个字符串。如果能剪出 $n$ 个或更多纸片，则输出 `YES`，否则输出 `NO`。 --------- translate by @[1289H2051N343O375S8](https://www.luogu.com.cn/user/45475)。

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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).

输入输出样例

输入样例 #1

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

输出样例 #1

YES
NO
YES
YES
YES

说明

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 $ .