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)

def solution(n, m, coins)
  coins.sort!
  coin_kind = m
  dp = Array.new(n+1).map{Array.new(coin_kind, 0)}
  coins.each_with_index do |coin, index|
    for sum in 0..n do
      tmp = []
      if index == 0 # coin == 1の時
        dp[sum][index] = sum / coin
        next
      end
      if sum == 0
        dp[sum][index] = 0
        next
      end
      dp[sum][index] = [(dp[sum - coin * (sum / coin)][index-1] + (sum/coin)), dp[sum][index - 1]].min
    end
  end
  dp.last.last
end

first_line = gets.split.map(&:to_i)
coins = gets.split.map(&:to_i)
p solution(first_line[0], first_line[1], coins)