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 Scala (judge verdict: Accepted)

object Main extends App {

  val Array(n, m) = io.StdIn.readLine.split(" ").map(_.toInt)
  val c = io.StdIn.readLine.split(" ").map(_.toInt)

  val ans = {
    val dp: Array[Int] = Array.fill[Int](n + 1)(Int.MaxValue)
    dp(0) = 0

    for {
      i <- 0 until m
      j <- c(i) to n
    } dp(j) = math.min(dp(j), dp(j - c(i)) + 1)

    dp(n)
  }

  println(ans)
}