CF1822D Super-Permutation

A permutation is a sequence $ n $ integers, where each integer from $ 1 $ to $ n $ appears exactly once. For example, $ [1] $ , $ [3,5,2,1,4] $ , $ [1,3,2] $ are permutations, while $ [2,3,2] $ , $ [4,3,1] $ , $ [0] $ are not. Given a permutation $ a $ , we construct an array $ b $ , where $ b_i = (a_1 + a_2 +~\dots~+ a_i) \bmod n $ . A permutation of numbers $ [a_1, a_2, \dots, a_n] $ is called a super-permutation if $ [b_1 + 1, b_2 + 1, \dots, b_n + 1] $ is also a permutation of length $ n $ . Grisha became interested whether a super-permutation of length $ n $ exists. Help him solve this non-trivial problem. Output any super-permutation of length $ n $ , if it exists. Otherwise, output $ -1 $ .

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