P9671 [ICPC 2022 Jinan R] Identical Parity

Let the value of a sequence be the sum of all numbers in it. Determine whether there exists a permutation of length $n$ such that the values of all subsegments of length $k$ of the permutation share the same parity. The values share the same parity means that they are all odd numbers or they are all even numbers. A subsegment of a permutation is a contiguous subsequence of that permutation. A permutation of length $n$ is a sequence in which each integer from $1$ to $n$ appears exactly once.

The first line contains one integer $T~(1\le T \le 10^5)$, the number of test cases. For each test case, the only line contains two integers $n,k~(1 \le k \le n \le 10^9)$.

For each test case, output $\texttt{Yes}$ (without quotes) if there exists a valid permutation, or $\texttt{No}$ (without quotes) otherwise. You can output $\texttt{Yes}$ and $\texttt{No}$ in any case (for example, strings $\texttt{YES}$, $\texttt{yEs}$ and $\texttt{yes}$ will be recognized as positive responses).

In the first test case, it can be shown that there does not exist any valid permutation. In the second test case, $[1,2,3,4]$ is one of the valid permutations. Its subsegments of length $2$ are $[1,2],[2,3],[3,4]$. Their values are $3,5,7$, respectively. They share the same parity. In the third test case, $[1,2,3,5,4]$ is one of the valid permutations. Its subsegments of length $3$ are $[1,2,3],[2,3,5],[3,5,4]$. Their values are $6,10,12$, respectively. They share the same parity.