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)

n, m = gets.chomp.split.map(&:to_i)
coins = gets.chomp.split.map(&:to_i).sort.reverse
coins.delete(1)
arr = (0..n).to_a
1.upto(n){|x|
    coins.each{|coin|
        q, r = x.divmod(coin)
        arr[x] = q + arr[r] if arr[x] > q + arr[r]
    }
}
puts arr[n]