Problem:
Coin Changing Problem

Find the minimum number of coins to make change for n cents using coins of denominations d1, d2,.., dm. The coins can be used any number of times.

Input

n m
d1 d2 ... dm

Two integers n and m are given in the first line. The available denominations are given in the second line.

Output

Print the minimum number of coins in a line.

Constraints

1 ≤ n ≤ 50000

1 ≤ m ≤ 20

1 ≤ denomination ≤ 10000

The denominations are all different and contain 1.

Sample Input 1

55 4
1 5 10 50

Sample Output 1

2

Sample Input 2

15 6
1 2 7 8 12 50

Sample Output 2

2

Sample Input 3

65 6
1 2 7 8 12 50

Sample Output 3

3

Solution in Haskell (judge verdict: Time Limit Exceeded)

import Control.Monad
import Data.Array.IO
import Data.List
import Data.Maybe

main = do
    [n,m] <- fmap (map read.words) getLine
    cs <- fmap (map read.words) getLine
    print =<< minCoinsI n cs
minCoinsI :: Int -> [Int] -> IO Int
minCoinsI j coins = do
    minarr <- newListArray (0,j) (repeat 0) :: IO (IOArray Int Int)
    forM_ coins $ \x -> do
        forM_ [0..j] $ \y -> do
            updateArray x y minarr
    return =<< readArray minarr j

updateArray :: Int -> Int -> IOArray Int Int -> IO ()
updateArray i j minarr
  | i == 1 = writeArray minarr j j
  | j == 0 = writeArray minarr j 0
  | otherwise = do
      left <- readArray minarr j
      right <- maybeReadArray minarr (j-i)
      let new = min left $ (fromMaybe (maxBound -1)right) + 1
      writeArray minarr j new

maybeReadArray arr ix = do
  (l,r) <- getBounds arr
  if (not (ix `elem` [l..r])) then return Nothing
                              else do
                                e <- readArray arr ix
                                return $ Just e