Rayan wants to present a gift to Reyhaneh to win her heart. However, Reyhaneh is particular and will only accept a k-harmonic set of permutations . We define a k-harmonic set of permutations as a set of (k) pairwise distinct permutations (p_1, p_2, \ldots, p_k) of size (n) such that for every pair of indices (i) and (j) (where (1 \leq i, j \leq n)), the following condition holds: () p_1i + p_2i + \ldots + p_ki = p_1j + p_2j + \ldots + p_kj () Your task is to help Rayan by either providing a valid k-harmonic set of permutations for given values of (n) and (k) or by determining that such a set does not exist. We call a sequence of length (n) a permutation if it contains every integer from (1) to (n) exactly once. The first line contains a single integer (t) ((1 \leq t \leq 1000)), the number of test cases. Each test case consists of two integers (n) and (k) ((1 \leq n, k \leq 10^5)). The sum of (n \cdot k) over all test cases does not exceed (5 \cdot 10^5). For each test case, if a k-harmonic set of permutations exists, print YES on the first line. Then, print (k) lines, each containing a distinct permutation of the integers from (1) to (n). If no such set exists, print NO on the first line. You can output "YES" and "NO" in any case (for example, strings "yEs", "yes", and "Yes" will be recognized as a positive response). If multiple answers are possible, you can output any of them. In example 1, we have (p_1 = 1, 2, 3), (p_2 = 2, 3, 1), and (p_3 = 3, 1, 2). It's easy to see that (p_11 + p_21 + p_31 = p_12 + p_22 + p_32 = p_13 + p_23 + p_33 = 6). In example 2, we have (p_1 = 1, 2, 3, 4) and (p_2 = 4, 3, 2, 1). It's easy to see that (p_11 + p_21 = p_12 + p_22 = p_13 + p_23 = p_14 + p_24 = 5). In example 3, as there are five distinct elements in (p_1), it's obvious that the answer is