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 {
  def main(args: Array[String]): Unit = {
    import scala.io.StdIn.readLine
    val Array(n, m) = readLine().split(' ').map(_.toInt)
    val coin = readLine().split(' ').map(_.toInt).sorted.reverse.toList

    val memo = Array.fill(n + 1, m + 1)(-1)

    def solve(money: Int, coin: List[Int], coinLength: Int): Int = {
      if (coinLength == 1) { // 1円しか残っていない時
        money
      } else if (memo(money)(coinLength) != -1) {
        memo(money)(coinLength)
      } else {
        val result = List(
          solve(money, coin.tail, coinLength - 1),
          if (money < coin.head) Int.MaxValue else 1 + solve(money - coin.head, coin, coinLength)
        ).min
        memo(money)(coinLength) = result
        result
      }
    }

    println(solve(n, coin, coin.length))
  }

}