Infinite Fence

题意翻译

## 题目描述 - 有一个长度为 $10^{100}$ 的栏杆，编号 $1,2,\dots,10^{100}$。 - 你要将编号为 $r$ 的倍数的栏杆染成红色，$b$ 的倍数的栏杆染成蓝色。 - 编号既是 $r$ 也是 $b$ 的栏杆染成蓝色或红色皆可。 - 其它栏杆不染色 - 将所有染色的栏杆按编号从小到大排序。 - 问：是否存在一种染色方法，使得不存在连续 $k$ 个被染色的栏杆，它们染上相同的颜色 ## 输入格式 **本题多测** 第一行一个整数 $T$ 表示测试数据组数。 接下来 $T$ 行每行三个整数 $r,g,b$ ## 输出格式 对于每组数据，如果可行输出 $\texttt{OBEY}$，否则输出 $\texttt{REBEL}$。 ## 数据范围 $1 \leq T \leq 1000$ $1 \leq r,g,k \leq 10^9$ 友情提醒：（基本）原题识别自动机：P6476

题目描述

You are a rebel leader and you are planning to start a revolution in your country. But the evil Government found out about your plans and set your punishment in the form of correctional labor. You must paint a fence which consists of $ 10^{100} $ planks in two colors in the following way (suppose planks are numbered from left to right from $ 0 $ ): - if the index of the plank is divisible by $ r $ (such planks have indices $ 0 $ , $ r $ , $ 2r $ and so on) then you must paint it red; - if the index of the plank is divisible by $ b $ (such planks have indices $ 0 $ , $ b $ , $ 2b $ and so on) then you must paint it blue; - if the index is divisible both by $ r $ and $ b $ you can choose the color to paint the plank; - otherwise, you don't need to paint the plank at all (and it is forbidden to spent paint on it). Furthermore, the Government added one additional restriction to make your punishment worse. Let's list all painted planks of the fence in ascending order: if there are $ k $ consecutive planks with the same color in this list, then the Government will state that you failed the labor and execute you immediately. If you don't paint the fence according to the four aforementioned conditions, you will also be executed. The question is: will you be able to accomplish the labor (the time is not important) or the execution is unavoidable and you need to escape at all costs.

输入输出格式

输入格式

The first line contains single integer $ T $ ( $ 1 \le T \le 1000 $ ) — the number of test cases. The next $ T $ lines contain descriptions of test cases — one per line. Each test case contains three integers $ r $ , $ b $ , $ k $ ( $ 1 \le r, b \le 10^9 $ , $ 2 \le k \le 10^9 $ ) — the corresponding coefficients.

输出格式

Print $ T $ words — one per line. For each test case print REBEL (case insensitive) if the execution is unavoidable or OBEY (case insensitive) otherwise.

输入输出样例

输入样例 #1

4
1 1 2
2 10 4
5 2 3
3 2 2

输出样例 #1

OBEY
REBEL
OBEY
OBEY