A. Farmer John's Challengetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputTrade Winds - Patrick Deng⠀Let's call an array a sorted if a_1 \leq a_2 \leq \ldots \leq a_{n - 1} \leq a_{n}.You are given two of Farmer John's favorite integers, n and k. He challenges you to find any array a_1, a_2, \ldots, a_{n} satisfying the following requirements:  1 \leq a_i \leq 10^9 for each 1 \leq i \leq n;  Out of the n total cyclic shifts of a, exactly k of them are sorted.^\dagger If there is no such array a, output -1.^\daggerThe x-th (1 \leq x \leq n) cyclic shift of the array a is a_x, a_{x+1} \ldots a_n, a_1, a_2 \ldots a_{x - 1}. If c_{x, i} denotes the i'th element of the x'th cyclic shift of a, exactly k such x should satisfy c_{x,1} \leq c_{x,2} \leq \ldots \leq c_{x, n - 1} \leq c_{x, n}.For example, the cyclic shifts for a = [1, 2, 3, 3] are the following:  x = 1: [1, 2, 3, 3] (sorted);  x = 2: [2, 3, 3, 1] (not sorted);  x = 3: [3, 3, 1, 2] (not sorted);  x = 4: [3, 1, 2, 3] (not sorted). InputThe first line contains t (1 \leq t \leq 10^3) — the number of test cases.Each test case contains two integers n and k (1 \leq k \leq n \leq 10^3) — the length of a and the number of sorted cyclic shifts a must have.It is guaranteed that the sum of n over all test cases does not exceed 10^3.OutputFor each test case, print a single line:   if there is a valid array a, output n integers, representing a_1, a_2, \ldots, a_{n};  otherwise, output -1. If there are multiple solutions, print any of them.ExampleInput
32 23 13 2Output
1 1
69420 69 420
-1
NoteIn the first testcase, a = [1, 1] satisfies n = 2, k = 2:The two cyclic shifts of a are [a_1, a_2] and [a_2, a_1], which are both [1, 1] and are sorted.In the second testcase, a = [69\,420, 69, 420] satisfies n = 3, k = 1:The three cyclic shifts of a are [a_1, a_2, a_3], [a_2, a_3, a_1], [a_3, a_1, a_2], which are [69\,420, 69, 420], [69, 420, 69\,420], and [420, 69\,420, 69], respectively. Only [69, 420, 69\,420] is sorted.
32 23 13 2
1 1 69420 69 420 -1 
['constructive algorithms', 'math', '*800']