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)
d = gets.split.map(&:to_i)
dp = Array.new(n+1,n)
dp[0] = 0
for i in 0..n
    m.times do |j|
        if n >= d[j]
            dp[i] = [dp[i],dp[i-d[j]]+1].min
        end
    end
end
puts dp[n]