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) · 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.
Input
The first line contains one integer t (1 ≤ t ≤ 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 ≤ n ≤ 2 · 10^5, 0 ≤ k ≤ 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 · 10^5.
Output
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 n2 lines output pairs of the split, in each line print 2 numbers — first the integer a, then the integer b.
Examples
Note
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) · 2 = 1 · (2 + 0) = 2 is not divisible by 4, so there is no partition.