Preparando MOJI
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 $$$b$$$.
44 12 012 1014 11
YES 1 2 3 4 NO YES 3 4 7 8 11 12 2 1 6 5 10 9 YES 1 2 3 4 5 6 7 8 9 10 11 12 13 14
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.
Informação
Provedor Codeforces
Código CF1719B
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Datas 09/05/2023 10:30:58
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