题目描述

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.

输入格式

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 $n,k~(1 \le k \le n \le 10^9)$.

输出格式

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).

题目大意

题目描述

定义一个序列的 权值 等于这个序列所有的元素之和。

试判断：是否存在一个长度为 $n$ 的 排列，满足以下约束条件？

• 其所有长度为 $k$ 的 子区间 的权值具有相同的奇偶性。

输入格式

第一行一个整数 $T$ $(1\leqslant T\leqslant 10^5)$，表示测试数据组数。

对于每组测试数据，仅有一行两个整数 $n,k$ $(1\leqslant k\leqslant n\leqslant 10^9)$，含义见“题目描述”。

输出格式

对于每组测试数据，输出一行一个字符串。若存在符合题意的排列，输出 $\texttt{Yes}$；否则，输出 $\texttt{No}$。

你可以以任意的大小写输出 $\texttt{Yes}$ 和 $\texttt{No}$（例如，$\texttt{YES}$，$\texttt{yEs}$ 和 $\texttt{yes}$ 都会被视作合法的输出）。

样例解释

对于第一组测试数据，能够证明不存在任何符合题意的排列。

对于第二组测试数据，$[1,2,3,4]$ 是一个符合题意的排列。其所有长度为 $2$ 的子区间分别为 $[1,2],[2,3],[3,4]$，它们的权值分别为 $3,5,7$，具有相同的奇偶性。

对于第三组测试数据，$[1,2,3,5,4]$ 是一个符合题意的排列。其所有长度为 $3$ 的子区间分别为 $[1,2,3],[2,3,5],[3,5,4]$，它们的权值分别为 $6,10,12$，具有相同的奇偶性。

3
3 1
4 2
5 3

No
Yes
Yes

提示

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.