Problem N
Hyper Smawk Bros

Image credits: EVO 2008 - Street Fighter IV. Image by Chris Ainsworth, licensed under CC BY 2.0.

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 $n \leq 0$. Determine whether you can force a win if Bob plays optimally.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \leq t \leq 10^4$). 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.

Output

For each test case, output $\texttt{YES}$ if you can force a win against Bob, and $\texttt{NO}$ otherwise.

Samples

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.

8
6 9
20 10
69 2
42 9
42 10
44 9
44 10
400000 400000

YES
YES
NO
NO
YES
YES
NO
YES