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: Runtime Error)

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 }

$count_map = {}
def solve i, n, count
  if !$count_map.has_key? i
    $count_map[i] = {}
  end

  if !$count_map[i].has_key? n
    $count_map[i][n] = count
  else
    $count_map[i][n] = $count_map[i][n] > count ? count : $count_map[i][n]
  end

  if n == 0
    return
  end

  if i == $m
    return
  end

  coin = $coin_list[i]
  tmp = n - coin
  if tmp >= 0
    solve i, tmp, count + 1
  end
  solve i + 1, n, count
end

solve 0, $n, 0

min_count = $n + 1
$count_map.each{|key, value|
  value.map.each{|left, count|
    if left == 0
      min_count = min_count > count ? count : min_count
    end
  }
}
puts min_count 

# def solve i, n, count
#   if n == 0
#     return count
#   end
#
#   if i == $m
#     return $n + 1
#   end
#
#   result1 = result2 = $n + 1
#   coin = $coin_list[i]
#   tmp = n - coin
#   if tmp >= 0
#     result2 = solve i, tmp, count + 1
#   end
#   result1 = solve i + 1, n, count
#
#   return [result1, result2].min
# end
#
# puts solve 0, $n, 0