# [USACO2011 Feb] Cow Line

时间限制：10s 空间限制：128MB

### 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.

有N头牛，分别用1……N表示，排成一行。

将N头牛，所有可能的排列方式，按字典顺序从小到大排列起来。

例如：有5头牛

1st: 1 2 3 4 5

2nd: 1 2 3 5 4

3rd: 1 2 4 3 5

4th : 1 2 4 5 3

5th : 1 2 5 3 4

……

现在，已知N头牛的排列方式，求这种排列方式的行号。

或者已知行号，求牛的排列方式。

所谓行号，是指在N头牛所有可能排列方式，按字典顺序从大到小排列后，某一特定排列方式所在行的编号。

如果，行号是3，则排列方式为1 2 4 3 5

如果，排列方式是 1 2 5 3 4 则行号为5

有K次问答，第i次问答的类型，由C_i来指明，C_i要么是‘P’要么是‘Q’。

当C_i为P时，将提供行号，让你答牛的排列方式。当C_i为Q时，将告诉你牛的排列方式，让你答行号。

### 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.

第1行：N和K

第2至2*K+1行：Line2*i ，一个字符‘P’或‘Q’，指明类型。

如果Line2*i是P，则Line2*i+1，是一个整数，表示行号；

如果Line2*i+1 是Q ，则Line2+i，是N个空格隔开的整数，表示牛的排列方式。

### 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.

第1至K行：如果输入Line2*i 是P，则输出牛的排列方式；如果输入Line2*i是Q，则输出行号

### 样例输入

5 2 P 3 Q 1 2 5 3 4

### 样例输出

1 2 4 3 5 5

### 提示

没有写明提示

### 题目来源

Silver