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)

#!/usr/bin/ruby
def ite(a,n)
	b = Array.new(n+1)
	b[0] = 0
	1.step(n){|m|
		i = 0
		k = -1
		a.size.times{|i|
			#p a[i]
			if m >= a[i] && b[m-a[i]] >= 0 && (k < 0 || b[m-a[i]] + 1 < k)
				k = b[m-a[i]] + 1
			end
		}
		b[m] = k
	}
	b[n]
end

n=gets.to_i
puts ite(gets.split.map(&:to_i),n)