# [Usaco2016 Dec]Team Building

### 题目描述

Every year, Farmer John brings his NN cows to compete for "best in show" at the state fair. His arch
-rival, Farmer Paul, brings his MM cows to compete as well (1≤N≤1000,1≤M≤1000).Each of the N+MN+
M cows at the event receive an individual integer score. However, the final competition this year wi
ll be determined based on teams of KK cows (1≤K≤10), as follows: Farmer John and Farmer Paul both
select teams of KK of their respective cows to compete. The cows on these two teams are then paired
off: the highest-scoring cow on FJ's team is paired with the highest-scoring cow on FP's team, the s
econd-highest-scoring cow on FJ's team is paired with the second-highest-scoring cow on FP's team, a
nd so on. FJ wins if in each of these pairs, his cow has the higher score.Please help FJ count the n
umber of different ways he and FP can choose their teams such that FJ will win the contest. That is,
each distinct pair (set of KK cows for FJ, set of KK cows for FP) where FJ wins should be counted.

(1 ≤ N ≤ 1000, 1 ≤ M ≤ 1000)。每只牛都有自己的分数。两人会选择K只牛组成队伍(1 ≤ K ≤ 10)，两队

### 输入格式

The first line of input contains N, M, and K. The value of K will be no larger than N or M.
The next line contains the N scores of FJ's cows.
The final line contains the M scores of FP's cows.

### 输出格式

Print the number of ways FJ and FP can pick teams such that FJ wins, modulo 1,000,000,009.

### 样例输入

```10 10 3
1 2 2 6 6 7 8 9 14 17
1 3 8 10 10 16 16 18 19 19```

`382`

### 题目来源

Platinum 鸣谢Firstlast提供译文