Problem F
Permutation
Input: Standard Input

Output: Standard Output

 

Given N and K find the N’th permutation of the integers from 1 to K when those permutations are lexicographically ordered.  N starts from 0. Since N is very large N will be represented by a sequence of K non-negative integers S1, S2 ,…, Sk. From this sequence of integers N can be calculated with the following expression.

 

 

Input

First line of the input contains T(≤10) the number of test cases. Each of these test cases consists of 2 lines. First line contains a integer K(1≤K≤50000). Next line contains K integers S1, S2 ,…, Sk.(0≤Si≤K-i).

 

Output

For each test case output contains N’th permutation of the integers from 1 to K. These K integers should be separated by a single space.

 

Sample Input                            Output for Sample Input

4
3
2 1 0
3
1 0 0
4
2 1 1 0
4
1 2 1 0

 

 
3 2 1
2 1 3
3 2 4 1
2 4 3 1

 

Problemsetter: Abdullah al Mahmud

Special Thanks: Manzurur Rahman Khan