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: Wrong Answer)

import java.util.Scanner;

class Main {
	static int count=0;
	public static void main(String args[]) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int m=in.nextInt();

		int[] c = new int[m];
		for (int i = 0; i < m; i++) {
			c[i] = in.nextInt();

		}
		if (solve(c,0,n)) {
			System.out.println(count);
		}


		in.close();
	}

	private static boolean solve(int[] c,int i, int m) {

	   if (m == 0) {

	     return true;
	   }
	   if (i == c.length) {
	     return false;
	   }
	   if(solve(c,i + 1, m) ) {
		   return true;
	   }else if( solve(c,i + 1, m - c[i])) {
		   count+=1;
		   return true;
	   }else {
		   return false;
	   }

	}
}