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 JAVA (judge verdict: Runtime Error)

import java.util.*;

public class Main {
	static int goal;

	static ArrayList<Integer> list = new ArrayList<>();
	static int[] cache;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		goal = sc.nextInt();

		int c = sc.nextInt();
		for (int i = 0; i < c; i++) {
			list.add(sc.nextInt());
		}
		cache = new int[goal + 1];

		System.out.println(compute(goal));
		sc.close();

	}

	public static int compute(int value) {
		if (cache[value] != 0) {
			return cache[value];
		}
		HashSet<Integer> set = new HashSet<Integer>();
		for (int e : list) {
			if (e == value) {
				cache[value] = 1;
				return 1;
			}
			if (e < value) {
				int coins = 1;
				coins += compute(value - e);
				set.add(coins);

			}
		}
		int result = Integer.MAX_VALUE;
		for (int e : set) {
			if (e < result) {
				result = e;
			}
		}
		cache[value] = result;
		return result;

	}

}