P15142 [SWERC 2025] Hyper Smawk Bros

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, you cannot use the same $x$ that your 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 $n \le 0$. 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 $n, m$ ($1 \le n \le 10^6$, $2 \le m \le 10^6$) — 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 **YES** if you can force a win against Bob, and **NO** otherwise. The judge is case-insensitive (for example, YES, Yes, yes, yEs will all be recognized as positive answers).

#### Explanation of sample 1. In the first test case, you can win immediately by dealing damage $8$, so that $n$ becomes $6 - 8 = -2 \le 0$. 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.