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)
d.sort!

dp=Array.new(50001,10000000)
dp[0]=0
for i in 0..n
    for j in 0..m-1
        if(i+d[j]>n)
            break
        end
       dp[i+d[j]]=[dp[i+d[j]],dp[i]+1].min
    
    end
end

p dp[n]