B"Petya got an array a of numbers from 1 to n , where a[i]=i . He performed n operations sequentially. In the end, he received a new state of the a array. At the i -th operation, Petya chose the first i elements of the array and cyclically shifted them to the right an arbitrary number of times (elements with indexes i+1 and more remain in their places). One cyclic shift to the right is such a transformation that the array a=[a_1, a_2, ... , a_n] becomes equal to the array a = [a_i, a_1, a_2, ... , a_{i-2}, a_{i-1}, a_{i+1}, a_{i+2}, ... , a_n] . For example, if a = [5,4,2,1,3] and i=3 (that is, this is the third operation), then as a result of this operation, he could get any of these three arrays: Let's look at an example. Let n=6 , i.e. initially a=[1,2,3,4,5,6] . A possible scenario is described below. You are given a final array state a after all n operations. Determine if there is a way to perform the operation that produces this result. In this case, if an answer exists, print the numbers of cyclical shifts that occurred during each of the n operations. The first line of the input contains an integer t ( 1 <= t <= 500 ) -- the number of test cases in the test. The descriptions of the test cases follow. The first line of the description of each test case contains one integer n ( 2 <= n <= 2 cdot10^3 ) -- the length of the array a . The next line contains the final state of the array a : n integers a_1, a_2, ... , a_n ( 1 <= a_i <= n ) are written. All a_i are distinct. It is guaranteed that the sum of n values over all test cases does not exceed 2 cdot10^3 . For each test case, print the answer on a separate line. Print -1 if the given final value a cannot be obtained by performing an arbitrary number of cyclic shifts on each operation. Otherwise, print n non-negati"...