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: Accepted)

n,m = gets.split(" ").map(&:to_i)
dp = Array.new(m){Array.new(n+1,0)}
coins = gets.split(" ").map(&:to_i)
#coins ??????
coins.each_with_index do |coin,index|
  #???????????????????????????
  (n+1).times do |value|
    #?????¨??????coin??????????????????????????????????¶???????????????????
    case
    when index >= 1 && value-coin > 0
      #???????????£?????????????????¨???
      dp[index][value] = [dp[index-1][value], dp[index][value-coin]+1].min
    when value-coin == 0
      #coin????????????????????????0??????1?????\??????
      dp[index][value] = 1
    when index == 0 && value-coin > 0
      #?????????????????????????????¨???
      dp[index][value] = dp[index][value-coin]+1
    when index >= 1 && !(value-coin > 0)
      #???????????£?????????????????¨???
      dp[index][value] = dp[index-1][value]
    end
  end
end
puts dp[m-1][n]