# [USACO11FEB]牛线Cow Line

## 题目描述

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. N(1<=N<=20)头牛，编号为1...N，正在与FJ玩一个疯狂的游戏。奶牛会排成一行（牛线），问FJ此时的行号是多少。之后，FJ会给牛一个行号，牛必须按照新行号排列成线。 行号是通过以字典序对行的所有排列进行编号来分配的。比如说：FJ有5头牛，让他们排为行号3，排列顺序为： 1：1 2 3 4 5 2：1 2 3 5 4 3：1 2 4 3 5 因此，牛将在牛线1 2 4 3 5中。 之后，奶牛排列为“1 2 5 3 4”，并向FJ问他们的行号。继续列表： 4：1 2 4 5 3 5：1 2 5 3 4 FJ可以看到这里的答案是5。 FJ和奶牛希望你的帮助玩他们的游戏。他们需要K(1<=K<=10000)组查询，查询有两个部分：C\_i将是“P”或“Q”的命令。 如果C\_i是'P'，则查询的第二部分将是一个整数A\_i（1 <= A\_i <= N！），它是行号。此时，你需要回答正确的牛线。 如果C\_i是“Q”，则查询的第二部分将是N个不同的整数B\_ij（1 <= B\_ij <= N）。这将表示一条牛线，此时你需要输出正确的行号。

## 输入输出格式

### 输入格式

\* 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.

### 输出格式

\* 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.

## 输入输出样例

### 输入样例 #1

``````5 2
P
3
Q
1 2 5 3 4
``````

### 输出样例 #1

``````1 2 4 3 5
5
``````