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#Post#: 34--------------------------------------------------
Ordering of Soldiers
By: ravu Date: August 18, 2012, 1:47 am
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As you are probably well aware, in Byteland it is always the
military officer's main worry to order his soldiers on parade
correctly. In Bitland ordering soldiers is not really such a
problem. If a platoon consists of n men, all of them have
different rank (from 1 - lowest to n - highest) and on parade
they should be lined up from left to right in increasing order
of rank.
Sounds simple, doesn't it? Well, Msgt Johnny thought the same,
until one day he was faced with a new command. He soon
discovered that his elite commandos preferred to do the
fighting, and leave the thinking to their superiors. So, when at
the first rollcall the soldiers lined up in fairly random order
it was not because of their lack of discipline, but simply
because they couldn't work out how to form a line in correct
order of ranks. Msgt Johnny was not at all amused, particularly
as he soon found that none of the soldiers even remembered his
own rank. Over the years of service every soldier had only
learned which of the other soldiers were his superiors. But Msgt
Johnny was not a man to give up easily when faced with a true
military challenge. After a moment's thought a solution of
brilliant simplicity struck him and he issued the following
order: "men, starting from the left, one by one, do: (step
forward; go left until there is no superior to the left of you;
get back in line).". This did indeed get the men sorted in a few
minutes. The problem was solved... for the time being.
The next day, the soldiers came in exactly the same order as the
day before, and had to be rearranged using the same method.
History repeated. After some weeks, Msgt Johnny managed to force
each of his soldiers to remember how many men he passed when
going left, and thus make the sorting process even faster.
If you know how many positions each man has to walk to the left,
can you try to find out what order of ranks the soldiers
initially line up in?
Input
The first line of input contains an integer t<=50, the number of
test cases. It is followed by t test cases, each consisting of 2
lines. The first line contains a single integer n
(1<=n<=200000). The second line contains n space separated
integers wi, denoting how far the i-th soldier in line must walk
to the left when applying Msgt Johnny's algorithm.
Output
For each test case, output a single line consisting of n space
separated integers - the ranks of the soldiers, given from left
to right in their initial arrangement.
Example
Input:
2
3
0 1 0
5
0 1 2 0 1
Output:
2 1 3
3 2 1 5 4
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