public class CoinCounting{
	public static void main (String[] args){
		CoinCounting c = new CoinCounting();
		int target = 5;
		int[] coinSizes = {1, 2, 5};
		System.out.println(c.coinCount(target, coinSizes));
	}

	private void generateWays(int coin, int target, int[] ways){
		for (int j = coin; j <= target; j++) {
			ways[j] += ways[j - coin];
		}
	}

	public int coinCount(int target, int[] coinSizes){
		int[] ways = new int[target+1];
		ways[0] = 1;

		for (int i = 0; i < coinSizes.length; i++) {
			generateWays(coinSizes[i], target, ways);
		}

		return ways[ways.length-1];
	}
}