22713_CowLine

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: C_i will be the command, which is either 'P' or 'Q'.

If C_i is 'P', then the second part of the query will be one integer A_i ( 1 ≤ A_i ≤ N! ), which is a line number. This is Farmer John challenging the cows to line up in the correct cow line.

If C_i is 'Q', then the second part of the query will be N distinct integers B_ij (1 ≤ B_ij ≤ N). This will denote a cow line. These are the cows challenging Farmer John to find their line number.

Multiple test cases. For each case:

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 B_ij which represent the cow line. If the line 2×i is 'P', then line 2×i+1 will contain a single integer A_i which is the line number to solve for.

For each case, output :

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.

Output a blank line after each case.

5 2
P
3
Q
1 2 5 3 4

1 2 4 3 5
5