Halloween Sale

You wish to buy video games from the famous online video game store Mist.

Usually, all games are sold at the same price, p dollars. However, they are planning to have the seasonal Halloween Sale next month in which you can buy games at a cheaper price. Specifically, the first game you buy during the sale will be sold at p dollars, but every subsequent game you buy will be sold at exactly d dollars less than the cost of the previous one you bought. This will continue until the cost becomes less than or equal to m dollars, after which every game you buy will cost m dollars each.

For example, if p = 20, d = 3 and m = 6, then the following are the costs of the first 11 games you buy, in order:

20, 17, 14, 11, 8, 6, 6, 6, 6, 6, 6

You have s dollars in your Mist wallet. How many games can you buy during the Halloween Sale?

Input Format

The first and only line of input contains four space-separated integers p, d, m and s.

Constraints

Output Format

Print a single line containing a single integer denoting the maximum number of games you can buy.

Sample Input 0

1

20 3 6 80

Sample Output 0

1

6

Explanation 0

We have p = 20, d = 3 and m = 6, the same as in the problem statement. We also have S = 80 dollars. We can buy 6 games since they cost 20 + 17 + 14 + 11 + 8 + 6 = 76 dollars. However, we cannot buy a 7th game. Thus, the answer is 6.

Sample Input 1

1

20 3 6 85

Sample Output 1

1

7

Explanation 1

This is the same as the previous case, except this time we have s = 85 dollars. This time, we can buy 7 games since they cost 20 + 17 + 14 + 11 + 8 + 6 + 6 = 82 dollars. However, we cannot buy an 8th game. Thus, the answer is 7.

Solution Accepted

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function howManyGames(p, d, m, s) {
  let restMoney = s;
  let price = p;
  let isDiscount = p - d >= m;
  let results = 0;

  if (restMoney > 0) {
    restMoney -= price;
    restMoney >= 0 && results++;
    isDiscount = price - d >= m;
  }

  while (restMoney > 0) {
    price = isDiscount ? price - d : m;
    restMoney = restMoney - price; 
    restMoney >= 0 && results++;
    isDiscount = price - d >= m;
  }

  return results;
}