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.

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 $ .

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 $ .

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.