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 OCaml (judge verdict: Accepted)

let solve c n m =
  let dp = Array.make_matrix (m + 1) (n + 1) max_int in
  for i = 1 to m do dp.(i).(0) <- 0 done;
  for i = 1 to m do
    for j = 1 to n do
      dp.(i).(j) <-
        if j - c.(i-1) < 0 then dp.(i-1).(j)
        else min dp.(i-1).(j) (dp.(i).(j - c.(i-1)) + 1)
    done
  done;
  dp.(m).(n)

let () =
  let n, m = Scanf.scanf "%d %d " (fun n m -> n, m) in
  let c = Array.init m (fun _ -> Scanf.scanf "%d " (fun i -> i)) in
  solve c n m |> Printf.printf "%d\n"