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)
  dp = [0] + [Float::INFINITY] * n
  for coin in coins
    for amount in 0..n
      if amount >= coin
        dp[amount] = [dp[amount], dp[amount - coin] + 1].min
      else
        dp[amount] = dp[amount]
      end
    end
    p dp
  end
  dp[n]
end


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