The N (1 <= N <= 20) cows conveniently numbered 1...N are playing yet another one of their crazy games with Farmer John. The cows will arrange themselves in a line and ask Farmer John what their line number is. In return, Farmer John can give them a line number and the cows must rearrange themselves into that line.
A line number is assigned by numbering all the permutations of the line in lexicographic order.
Consider this example:
Farmer John has 5 cows and gives them the line number of 3.
The permutations of the line in ascending lexicographic order: 1st: 1 2 3 4 5
2nd: 1 2 3 5 4
3rd: 1 2 4 3 5
Therefore, the cows will line themselves in the cow line 1 2 4 3 5.
The cows, in return, line themselves in the configuration '1 2 5 3 4' and ask Farmer John what their line number is.
Continuing with the list:
4th : 1 2 4 5 3
5th : 1 2 5 3 4
Farmer John can see the answer here is 5
Farmer John and the cows would like your help to play their game. They have K (1 <= K <= 10,000) queries that they need help with. Query i has two parts: will be the command, which is either 'P' or 'Q'.
If is 'P', then the second part of the query will be one integer (1 <= <= N!), which is a line number. This is Farmer John challenging the cows to line up in the correct cow line.
If is 'Q', then the second part of the query will be N distinct integers (1 <= <= N). This will denote a cow line. These are the cows challenging Farmer John to find their line number.

* Line 1: Two space-separated integers: N and K
* Lines 2..2*K+1: Line 2*i and 2*i+1 will contain a single query.
Line 2*i will contain just one character: 'Q' if the cows are lining up and asking Farmer John for their line number or 'P' if Farmer John gives the cows a line number.
If the line 2*i is 'Q', then line 2*i+1 will contain N space-separated integers  which represent the cow line. If the line 2*i is 'P', then line 2*i+1 will contain a single integer  which is the line number to solve for.

* Lines 1..K: Line i will contain the answer to query i.
If line 2*i of the input was 'Q', then this line will contain a single integer, which is the line number of the cow line in line 2*i+1.
If line 2*i of the input was 'P', then this line will contain N space separated integers giving the cow line of the number in line 2*i+1.

5 2 
P 
3 
Q 
1 2 5 3 4 

1 2 4 3 5
5