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 Ruby (judge verdict: Wrong Answer)

count = 0
$n = 0
$m = 0
coin_str = ""
STDIN.each_line {|line|
  if count == 0
    count = 1
    n_m = line.split " "
    $n = n_m[0].to_i
    $m = n_m[1].to_i
    next
  end

  coin_str = line
}

$memo = {}

$coin_list = coin_str.split " "
$result = 0
def solve i, n, count
  if i == $m
    return $m + 1
  end

  if n == 0
    return count
  end

  if !$memo.has_key? (i + 1)
    $memo[i + 1] = {}
  end

  if !$memo.has_key? (i)
    $memo[i] = {}
  end

  count1 = count2 = count3 = count4 = $m + 1
  if $memo[i + 1].has_key? (n)
    count2 = $memo[i + 1][n]
  else
    $memo[i + 1][n] = count2 = solve i + 1, n, count
  end


  coin = $coin_list[i].to_i
  tmp = n - coin
  if tmp >= 0
    if $memo[i].has_key? (tmp)
      count3 = $memo[i][tmp]
    else
      $memo[i][tmp] = count3 = solve i, tmp, count + 1
    end

    if $memo[i + 1].has_key? (tmp)
      count4 = $memo[i + 1][tmp]
    else
      $memo[i + 1][tmp] = count4 = solve i + 1, tmp , count + 1
    end

  end

  list = [count1, count2, count3, count4]
  return list.min
end

puts solve 0, $n, 0