# P3014 [USACO11FEB]牛线Cow Line

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• 660提交
• 题目提供者 FarmerJohn2
• 评测方式 云端评测
• 标签 动态规划,动规,dp 枚举,暴力 贪心 USACO 2011
• 难度 普及+/提高
• 时空限制 1000ms / 128MB
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## 题目背景

征求翻译。如果你能提供翻译或者题意简述，请直接发讨论，感谢你的贡献。

## 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： 复制
5 2
P
3
Q
1 2 5 3 4

输出样例#1： 复制
1 2 4 3 5
5


## 说明

感谢@prcups 提供翻译

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