CF2106B St. Chroma

Given a permutation $ ^{\text{∗}} $ $ p $ of length $ n $ that contains every integer from $ 0 $ to $ n-1 $ and a strip of $ n $ cells, St. Chroma will paint the $ i $ -th cell of the strip in the color $ \operatorname{MEX}(p_1, p_2, ..., p_i) $ $ ^{\text{†}} $ . For example, suppose $ p = [1, 0, 3, 2] $ . Then, St. Chroma will paint the cells of the strip in the following way: $ [0, 2, 2, 4] $ . You have been given two integers $ n $ and $ x $ . Because St. Chroma loves color $ x $ , construct a permutation $ p $ such that the number of cells in the strip that are painted color $ x $ is maximized. $ ^{\text{∗}} $ A permutation of length $ n $ is a sequence of $ n $ elements that contains every integer from $ 0 $ to $ n-1 $ exactly once. For example, $ [0, 3, 1, 2] $ is a permutation, but $ [1, 2, 0, 1] $ isn't since $ 1 $ appears twice, and $ [1, 3, 2] $ isn't since $ 0 $ does not appear at all. $ ^{\text{†}} $ The $ \operatorname{MEX} $ of a sequence is defined as the first non-negative integer that does not appear in it. For example, $ \operatorname{MEX}(1, 3, 0, 2) = 4 $ , and $ \operatorname{MEX}(3, 1, 2) = 0 $ .

The first line of the input contains a single integer $ t $ ( $ 1 \le t \le 4000 $ ) — the number of test cases. The only line of each test case contains two integers $ n $ and $ x $ ( $ 1 \le n \le 2 \cdot 10^5 $ , $ 0 \le x \le n $ ) — the number of cells and the color you want to maximize. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

Output a permutation $ p $ of length $ n $ such that the number of cells in the strip that are painted color $ x $ is maximized. If there exist multiple such permutations, output any of them.

The first example is explained in the statement. It can be shown that $ 2 $ is the maximum amount of cells that can be painted in color $ 2 $ . Note that another correct answer would be the permutation $ [0, 1, 3, 2] $ . In the second example, the permutation gives the coloring $ [0, 0, 0, 4] $ , so $ 3 $ cells are painted in color $ 0 $ , which can be shown to be maximum.