CF1758C Almost All Multiples

Given two integers $ n $ and $ x $ , a permutation $ ^{\dagger} $ $ p $ of length $ n $ is called funny if $ p_i $ is a multiple of $ i $ for all $ 1 \leq i \leq n - 1 $ , $ p_n = 1 $ , and $ p_1 = x $ . Find the lexicographically minimal $ ^{\ddagger} $ funny permutation, or report that no such permutation exists. $ ^{\dagger} $ A permutation of length $ n $ is an array consisting of each of the integers from $ 1 $ to $ n $ exactly once. $ ^{\ddagger} $ Let $ a $ and $ b $ be permutations of length $ n $ . Then $ a $ is lexicographically smaller than $ b $ if in the first position $ i $ where $ a $ and $ b $ differ, $ a_i < b_i $ . A permutation is lexicographically minimal if it is lexicographically smaller than all other permutations.

The input consists of multiple test cases. The first line contains an integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. The description of the test cases follows. The only line of each test case contains two integers $ n $ and $ x $ ( $ 2 \leq n \leq 2 \cdot 10^5 $ ; $ 1 < x \leq n $ ). The sum of $ n $ across all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, if the answer exists, output $ n $ distinct integers $ p_1, p_2, \dots, p_n $ ( $ 1 \leq p_i \leq n $ ) — the lexicographically minimal funny permutation $ p $ . Otherwise, output $ -1 $ .

In the first test case, the permutation $ [3,2,1] $ satisfies all the conditions: $ p_1=3 $ , $ p_3=1 $ , and: - $ p_1=3 $ is a multiple of $ 1 $ . - $ p_2=2 $ is a multiple of $ 2 $ . In the second test case, the permutation $ [2,4,3,1] $ satisfies all the conditions: $ p_1=2 $ , $ p_4=1 $ , and: - $ p_1=2 $ is a multiple of $ 1 $ . - $ p_2=4 $ is a multiple of $ 2 $ . - $ p_3=3 $ is a multiple of $ 3 $ . We can show that these permutations are lexicographically minimal. No such permutations exist in the third test case.