CF1942A Farmer John's Challenge

[Trade Winds - Patrick Deng](https://soundcloud.com/patrick-deng-392681004/trade-winds-ft-alex-zhu) ⠀ 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 $ . $ ^\dagger $ The $ 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).

The 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 $ .

For 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.

In 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.