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: Time Limit Exceeded)

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
}

$coin_list = coin_str.split " "
$coin_list.map! {|item| item.to_i }
$coin_list.sort! {|a, b| b <=> a }
# $coin_list.delete (1)

$min_count = $n + 1
$coin_list.each do |num|
  if num == 1
    next
  end

  if $n < num
    next
  end

  tmp1 = $n / num
  tmp2 = $n % num
  count = tmp1 + tmp2
  $min_count = $min_count > count ? count : $min_count
end

def solve i, n, count
  if n == 0
    $min_count = $min_count > count ? count : $min_count;
    return $min_count
  end

  coin = $coin_list[i]
  if coin == 1
    result = count + n
    $min_count = $min_count > result ? result : $min_count;
    return $min_count
  end

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

  if count > $min_count
    return $min_count
  end

  result1 = result2 = $n + 1

  tmp = n - coin
  if tmp >= 0
    result2 = solve i, tmp, count + 1
    $min_count = $min_count > result2 ? result2 : $min_count;
  end

  result1 = solve i + 1, n, count
  $min_count = $min_count > result1 ? result1 : $min_count;
  return [result1, result2].min
end

puts solve 0, $n, 0