Problem:
Score : 200 points

Problem Statement

Some number of chocolate pieces were prepared for a training camp.
The camp had N participants and lasted for D days.
The i-th participant (1 \leq i \leq N) ate one chocolate piece on each of the following days in the camp: the 1-st day, the (A_i + 1)-th day, the (2A_i + 1)-th day, and so on.
As a result, there were X chocolate pieces remaining at the end of the camp. During the camp, nobody except the participants ate chocolate pieces.

Find the number of chocolate pieces prepared at the beginning of the camp.

Constraints

1 \leq N \leq 100

1 \leq D \leq 100

1 \leq X \leq 100

1 \leq A_i \leq 100 (1 \leq i \leq N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
D X
A_1
A_2
:
A_N

Output

Find the number of chocolate pieces prepared at the beginning of the camp.

Sample Input 1

3
7 1
2
5
10

Sample Output 1

8

The camp has 3 participants and lasts for 7 days.
Each participant eats chocolate pieces as follows:

The first participant eats one chocolate piece on Day 1, 3, 5 and 7, for a total of four.

The second participant eats one chocolate piece on Day 1 and 6, for a total of two.

The third participant eats one chocolate piece only on Day 1, for a total of one.

Since the number of pieces remaining at the end of the camp is one, the number of pieces prepared at the beginning of the camp is 1 + 4 + 2 + 1 = 8.

Sample Input 2

2
8 20
1
10

Sample Output 2

29

Sample Input 3

5
30 44
26
18
81
18
6

Sample Output 3

56

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import System.Environment
import Data.Maybe
import Data.List
import Control.Exception

main :: IO ()
main = do
  isTest <- getEnv "TEST" `catch` (\(SomeException _) -> return "")
  if isTest == "1"
    then do
      testFile <- readFile "tests"
      putStrLn $ tests testFile
    else do
      input <- getContents
      putStrLn $ trim (solve (trim input))

--処理
solve :: String -> String
solve s =
  show
    $ x
    + ( sum
      . fmap (\a -> (length . takeWhile (<=d) . fmap (\x -> x * a + 1)) [0 ..])
      )
        list
 where
  (line1:line2:line3) = lines s
  n                   = read line1 :: Int
  [d, x]              = fmap read (words line2) :: [Int]
  list                = fmap read line3 :: [Int]

tests :: String -> String
tests text = case testParse text of
  Right bodys -> unlines (fmap (\(i, body) -> test i body) (zip [1 ..] bodys))
  Left  msg   -> "Test file parse error:" ++ msg

test :: Int -> (String, String) -> String
test n (input, outputRight)
  | output == outputRight
  = header ++ "Passed"
  | otherwise
  = header
    ++ "Faild\n"
    ++ "Right:"
    ++ show outputRight
    ++ "\nOutput:"
    ++ show output
 where
  header = "test" ++ show n ++ ":"
  output = trim $ solve input

testParse :: String -> Either String [(String, String)]
testParse s = case lines s of
  (sp1:sp2:bodys) -> testBodysParse sp1 sp2 bodys
  _               -> Left "testParse"

testBodysParse
  :: String -> String -> [String] -> Either String [(String, String)]
testBodysParse sp1 sp2 = (traverse . testBodyParse) sp2 . (split sp1)

testBodyParse :: String -> [String] -> Either String (String, String)
testBodyParse sp body = case fmap (trim . unlines) (split sp body) of
  [input, output] -> Right (input, output)
  _               -> Left "testBodyParse"

split :: Eq a => a -> [a] -> [[a]]
split spratar = foldr f [[]]
 where
  f x (p:ps) | x == spratar = [] : p : ps
             | otherwise    = (x : p) : ps
  f _ _ = undefined

trimHead :: String -> String
trimHead = dropWhile (\s -> isJust (elemIndex s [' ', '\t', '\n', '\r']))

trim :: String -> String
trim = reverse . trimHead . reverse . trimHead