B'You are given a permutation ^ dagger a of size n . We call an index i good if a_i=i is satisfied. After each second, we rotate all indices that are not good to the right by one position. Formally, For each i from 1 to n , find the first time that index i becomes good. ^ dagger A permutation 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). Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= t <= 10^4 ). The description of the test cases follows. The first line of each test case contains a single integer n ( 1 <= n <= 10^6 ) -- the size of permutation a . The second line of each test case contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= n ) -- the elements of permutation a . It is guaranteed that the sum of n over all test cases does not exceed 10^6 . For each test case, output a single line containing n integers where the i -th integer represents the first time that index i becomes good. In the first test case, 2 and 5 are already in the correct position so indices 2 and 5 become good at 0 second. After 1 second, a cyclic shift will be done with s=[1, 3, 4] , resulting in array a=[1, 2, 3, 4, 5] . Notice that indices 1 , 3 and 4 become good at 1 second. In the second test case, 5 is already in the correct position, so index 5 becomes good at 0 second. After 1 second, a cyclic shift will be done with s=[1, 2, 3, 4, 6] , resulting in array a=[3, 2, 1, 4, 5, 6] . Notice that indices 2 , 4 and 6$$'...