CF2157I Hyper Smawk Bros

[Vicious Hobo - Break the Targets](https://soundcloud.com/moogle-knights-5-wryyyyy/ez-pz-lemongrab) ⠀ You and Bob are playing Hyper Smawk Bros against each other, facing a single boss with health $ n $ . You and Bob act alternately, and you start. On your turn, you may use an attack that deals an integer amount of damage $ x $ in $ [1, m] $ , replacing $ n $ with $ n - x $ . However, one cannot use the same $ x $ that his opponent just used on the previous turn (on the very first move of the game, any $ x $ in $ [1, m] $ is allowed). The winner is the first player to reduce the boss's health to $ n \leq 0 $ . Determine whether you can force a win if Bob plays optimally.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The only line of each test case contains two integers $ n $ , $ m $ ( $ 1 \le n \le 10^6 $ , $ 2 \leq m \leq 10^6 $ ) — the starting health $ n $ and the maximum damage per attack $ m $ . Note that there are no constraints on the sum of $ n $ over all test cases, and there are no constraints on the sum of $ m $ over all test cases.

For each test case, output $ \texttt{YES} $ if you can force a win against Bob, and $ \texttt{NO} $ otherwise. The judge is case-insensitive (for example, $ \texttt{YES} $ , $ \texttt{Yes} $ , $ \texttt{yes} $ , $ \texttt{yEs} $ will all be recognized as positive answers).

In the first test case, you can win immediately by dealing damage $ 8 $ , so that $ n $ becomes $ 6-8 = -2 \leq 0 $ . In the second test case, - you choose to deal damage $ 10 $ ; - Bob can choose to deal any damage in $ [1, 10] $ different from $ 10 $ ; - then you can choose to deal damage $ 10 $ and win. In the third test case, - either you start by dealing damage $ 1 $ , then Bob must deal damage $ 2 $ , then you must deal damage $ 1 $ , etc.; - or you start by dealing damage $ 2 $ , then Bob must deal damage $ 1 $ , then you must deal damage $ 2 $ , etc. In both cases, you lose.