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
  end

  coin_str = line
}

$mem = {}
$coin_list = coin_str.split " "
$min_count = $n + 1
def solve i, n, count
  if n == 0
    return count
  end

  if i == $m
    return $n + 1
  end

  result1 = result2 = result3 = $n + 1
  if !$mem.has_key? (i)
    $mem[i] = {}
  end
  
  if !$mem.has_key? (i + 1)
    $mem[i + 1] = {}
  end

  if $mem[i + 1].has_key? (n)
    result1 = $mem[i + 1][n]
  elsif
    $mem[i + 1][n] = result1 = solve(i + 1, n, count)
  end

  tmp = n - $coin_list[i].to_i
  if tmp >= 0
    if $mem[i + 1].has_key? (tmp)
      result2 = $mem[i + 1][tmp]
    elsif
      $mem[i + 1][tmp] = result2 = solve(i + 1, tmp, count + 1)
    end

    if $mem[i].has_key? (tmp)
      result3 = $mem[i][tmp]
    elsif
      $mem[i][tmp] = result3 = solve(i, tmp, count + 1)
    end
  end

  return [result1, result2, result3].min
end

puts solve 0, $n, 0