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)

line = gets
num = line.split(" ")
n,m = num[0].to_i , num[1].to_i
line = gets
coin = []
coin = line.split(" ")
dp = Array.new(50001,100000000)
dp[0] = 0
n.times{|i|
	m.times{|j|
		nx = coin[j].to_i + i.to_i
		dp[nx] = dp[nx] > dp[i] + 1 ? dp[i] + 1 : dp[nx] if nx <= n
	}
}
p dp[n]