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.Reader
import Data.Array.IArray

main = do
    [n,m] <- fmap (map read.words) getLine
    cs <- fmap (map read.words) getLine
    let coins = array (1,m) $ zip [1..] cs
    print $ runReader (minCoinsR m n) coins

minCoinsR :: Int -> Int -> Reader (Array Int Int) Int
minCoinsR i j
  | j < 0 = return (maxBound - 1)
  | j == 0 = return 0
  | i == 1 = return j
  | otherwise = do
       arr <- ask
       l <- minCoinsR (i-1) j
       r <- minCoinsR i (j-arr!i)
       return $ min l (r+1)