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.chomp.split(" ").map{|item| item.to_i}
c = gets.chomp.split(" ").map{|item| item.to_i}
t = Array.new(n,50000)
t.unshift(0)
for i in 0..(m-1) do
	for j in c[i]..n do
		t[j] = (t[j] <= t[j-c[i]]+1) ? t[j] : t[j-c[i]]+1
	end
end
print("#{t[n]}\n")