CF1719B.Mathematical Circus

A new entertainment has appeared in Buryatia — a mathematical circus! The magician shows two numbers to the audience — $n$ and $k$, where $n$ is even. Next, he takes all the integers from $1$ to $n$, and splits them all into pairs $(a, b)$ (each integer must be in exactly one pair) so that for each pair the integer $(a + k) \cdot b$ is divisible by $4$ (note that the order of the numbers in the pair matters), or reports that, unfortunately for viewers, such a split is impossible.

Burenka really likes such performances, so she asked her friend Tonya to be a magician, and also gave him the numbers $n$ and $k$.

Tonya is a wolf, and as you know, wolves do not perform in the circus, even in a mathematical one. Therefore, he asks you to help him. Let him know if a suitable splitting into pairs is possible, and if possible, then tell it.

布里亚特地区出现了一种新型娱乐活动——数学马戏团！魔术师向观众展示两个数：$n$ 和 $k$，其中 $n$ 为偶数。接着，他取出从 $1$ 到 $n$ 的所有整数，并将它们全部两两配对成形如 $(a, b)$ 的有序对（每个整数必须且仅能出现在一个有序对中），使得对每个有序对，整数 $(a + k) \cdot b$ 都能被 $4$ 整除（注意：有序对中数字的顺序是重要的）；若这样的配对方式不存在，则魔术师会遗憾地告知观众该配对不可行。

布伦卡非常喜爱这类表演，于是她请朋友托尼娅担任魔术师，并把数字 $n$ 和 $k$ 告诉了他。

托尼娅是一只狼，而众所周知，狼绝不会在马戏团中表演——哪怕是在数学马戏团中也不例外。因此，他请你来帮忙：请告诉他是否存在满足条件的配对方案；若存在，请给出一种具体方案。

The first line contains one integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. The following is a description of the input data sets.

The single line of each test case contains two integers $n$ and $k$ ($2 \leq n \leq 2 \cdot 10^5$, $0 \leq k \leq 10^9$, $n$ is even) — the number of integers and the number being added $k$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \leq t \leq 10^4$）—— 表示测试用例的数量。接下来是对各组输入数据的描述。

每个测试用例仅有一行，包含两个整数 $n$ 和 $k$（$2 \leq n \leq 2 \cdot 10^5$，$0 \leq k \leq 10^9$，且 $n$ 为偶数）—— 分别表示整数的个数以及被加数 $k$。

保证所有测试用例中 $n$ 的总和不超过 $2 \cdot 10^5$。

For each test case, first output the string "YES" if there is a split into pairs, and "NO" if there is none.

If there is a split, then in the following $\frac{n}{2}$ lines output pairs of the split, in each line print $2$ numbers — first the integer $a$, then the integer $b$.

对于每个测试用例，如果存在一种配对划分方式，则首先输出字符串 "YES"；否则输出 "NO"。

如果存在配对划分，则在接下来的 $\frac{n}{2}$ 行中输出该划分的各对数，每行输出 $2$ 个整数 —— 先输出整数 $a$，再输出整数 $b$。

In the first test case, splitting into pairs $(1, 2)$ and $(3, 4)$ is suitable, same as splitting into $(1, 4)$ and $(3, 2)$.

In the second test case, $(1 + 0) \cdot 2 = 1 \cdot (2 + 0) = 2$ is not divisible by $4$, so there is no partition.

在第一个测试用例中，划分为 $(1, 2)$ 和 $(3, 4)$ 是可行的，划分为 $(1, 4)$ 和 $(3, 2)$ 同样可行。

在第二个测试用例中，$(1 + 0) \cdot 2 = 1 \cdot (2 + 0) = 2$ 不能被 $4$ 整除，因此不存在满足条件的划分。