시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 512 MB35282583.333%

## 문제

Cesar and Raul like betting and good food, in no particular order. They want to try out a new fancy restaurant and they decided to make a bet - they are going to play a game the loser pays for dinner.

They have a box with N balls. Each ball contains a distinct number between 1 and N. Then, the game proceeds with these steps:

• Initially, each person picks C distinct numbers between 1 and N and writes them down on a separate card.
• In each round, D balls are drawn from the box uniformly at random. Cesar and Raul mark down the ball numbers that appear in their respective card. The D balls are then returned to the box.
• The game stops when a player is able to mark on the card all the numbers he chose. That player is the winner. If both players finish at the same time, it tis a draw and they will split the dinner.

They are quite eager to try out this new restaurant and they're now wondering: how many rounds will the game last?

Given the number N of balls, the number aD of balls they sraw from the box in each round, the amount C of numbers in theis cards and the numbers they wrote down, find the expected number of rounds the game will last.

## 입력

The first line of the input consists of three space separated integers: N, D, and C. N is the number of balls, D is the number of balls drawn in each round, and C is the cards' size. Each of the following two lines contains C space separated integers: the number Cesar and Raul wrote down, respectively.

## 출력

The output is the expected number of rounds of the game.

The result will be considered correct as long as the absolute error does not exceed 10-3.

## 제한

• 1 ≤ N ≤ 50 Number of balls in the box
• 1 ≤ D ≤ min(10,N) Number of balls drawn in each round
• 1 ≤ C ≤ min(10,N) Cards' size

## 예제 입력 1

2 1 1
1
2


## 예제 출력 1

1.00000


## 예제 입력 2

30 5 10
2 3 5 7 11 13 17 19 23 29
20 18 16 14 12 10 8 6 4 2


## 예제 출력 2

13.30378