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)

#Coin Changing Problem

n,m = STDIN.gets.split(" ").collect{|e| e.to_i}
@ds = STDIN.gets.split(" ").collect{|e| e.to_i}

#n = 55
#m = 4
#@ds = [1,5,10,50]
@dp = Array.new(m,Array.new(n))
@max = m
def rec(index,left)
#    [index,left].each do |e|
#       print e,"," 
#    end
#    puts ""
    return 0 if left == 0
    return 50000 if index == @max
    return @dp[index][left] unless @dp[index][left] == nil

    
    v1 = rec(index + 1, left - @ds[index]) + 1 # include
    v2 = rec(index + 1, left) # not include
    v = [v1,v2].min

    @dp[index][left] = v
    return v
end

puts rec(0,n)