I. Hyper Smawk Bros
time limit per test
4 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output
Vicious Hobo - Break the Targets
⠀

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.

Input

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.

Output

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).

Example
Input
8
6 9
20 10
69 2
42 9
42 10
44 9
44 10
400000 400000
Output
YES
YES
NO
NO
YES
YES
NO
YES
Note

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.