Description

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.
Print your answer modulo 1,000,000,009.
每年农夫约翰都会带着他的N只牛去集会上参加“你是最棒哒“的比赛。他的对手农夫保罗也带了M只牛去参加比赛
(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
牛在按分数大小排序后一一配对,并且约翰打败保罗当且仅当对于每一对牛,约翰的牛分数都比保罗的高。请帮助
约翰计算约翰打败保罗的方案数 mod 1000000009。两种方案不同,当且仅当约翰或保罗选择的牛的集合与另一种
方案不同。

Input

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.

Output

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

Sample Input

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

Sample Output

382

HINT

Source

Platinum 鸣谢Firstlast提供译文

设dp[i][j]k]前i头fj的牛 j头fp的牛 配对k次的方案数

考虑dp[i+1][j][k]->dp[i+1][j+1][k]

dp[i][j+1][k]->dp[i+1][j+1][k]会算重复 所以减去即可

 

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