CF2035H Peak Productivity Forces

I'm peakly productive and this is deep. You are given two permutations $ ^{\text{∗}} $ $ a $ and $ b $ , both of length $ n $ . You can perform the following three-step operation on permutation $ a $ : 1. Choose an index $ i $ ( $ 1 \le i \le n $ ). 2. Cyclic shift $ a_1, a_2, \ldots, a_{i-1} $ by $ 1 $ to the right. If you had chosen $ i = 1 $ , then this range doesn't exist, and you cyclic shift nothing. 3. Cyclic shift $ a_{i + 1}, a_{i + 2}, \ldots, a_n $ by $ 1 $ to the right. If you had chosen $ i = n $ , then this range doesn't exist, and you cyclic shift nothing. After the operation, $ a_1,a_2,\ldots, a_{i-2},a_{i-1},a_i,a_{i + 1}, a_{i + 2},\ldots,a_{n-1}, a_n $ is transformed into $ a_{i-1},a_1,\ldots,a_{i-3},a_{i-2},a_i,a_n, a_{i + 1},\ldots,a_{n-2}, a_{n-1} $ . Here are some examples of operations done on the identity permutation $ [1,2,3,4,5,6,7] $ of length $ 7 $ : - If we choose $ i = 3 $ , it will become $ [2, 1, 3, 7, 4, 5, 6] $ . - If we choose $ i = 1 $ , it will become $ [1, 7, 2, 3, 4, 5, 6] $ . - If we choose $ i = 7 $ , it will become $ [6, 1, 2, 3, 4, 5, 7] $ . Notably, position $ i $ is not shifted. Find a construction using at most $ 2n $ operations to make $ a $ equal to $ b $ or print $ -1 $ if it is impossible. The number of operations does not need to be minimized. It can be shown that if it is possible to make $ a $ equal to $ b $ , it is possible to do this within $ 2n $ operations. $ ^{\text{∗}} $ A permutation of length $ n $ is an array consisting of $ n $ distinct integers from $ 1 $ to $ n $ in arbitrary order. For example, $ [2,3,1,5,4] $ is a permutation, but $ [1,2,2] $ is not a permutation ( $ 2 $ appears twice in the array), and $ [1,3,4] $ is also not a permutation ( $ n=3 $ but there is $ 4 $ in the array).

The first line contains a single integer $ t $ ( $ 1 \le t \le 5 \cdot 10^4 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 5 \cdot 10^5 $ ) — the lengths of permutations $ a $ and $ b $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le n $ ) — the values of permutation $ a $ . The third line of each test case contains $ n $ integers $ b_1, b_2, \ldots, b_n $ ( $ 1 \le b_i \le n $ ) — the values of permutation $ b $ . It is guaranteed that the sum of $ n $ over all test cases will not exceed $ 5 \cdot 10^5 $ .

For each test case: If there is a sequence of operations to transform $ a $ into $ b $ , output a single integer $ q $ ( $ 0\le q\le 2n $ ) — the number of operations in the first line and $ q $ integers with the $ i $ -th number representing the index of the $ i $ -th operation in the second line. If there is no sequence of operations, output $ -1 $ in the only line.

In the first case, you can do no operation since $ a=b $ . In the second case, it can be proved $ a $ can not be transformed into $ b $ . In the third case, $ a $ is transformed into $ [2,3,1] $ after the first operation and into $ b $ after the second operation.