Problem:
Score : 200 points

Problem Statement

Snuke has come to a store that sells boxes containing balls. The store sells the following three kinds of boxes:

Red boxes, each containing R red balls

Green boxes, each containing G green balls

Blue boxes, each containing B blue balls

Snuke wants to get a total of exactly N balls by buying r red boxes, g green boxes and b blue boxes.
How many triples of non-negative integers (r,g,b) achieve this?

Constraints

All values in input are integers.

1 \leq R,G,B,N \leq 3000

Input

Input is given from Standard Input in the following format:

R G B N

Output

Print the answer.

Sample Input 1

1 2 3 4

Sample Output 1

4

Four triples achieve the objective, as follows:

(4,0,0)

(2,1,0)

(1,0,1)

(0,2,0)

Sample Input 2

13 1 4 3000

Sample Output 2

87058

Solution in Ruby (2.3.3) (judge verdict: Accepted)

r, g, b, n = gets.split.map(&:to_i)
r, g, b = [r, g, b].sort!

ans = 0

0.upto(n / r) do |x|
  balls = r * x
  next if balls > n
  if balls == n
    ans += 1
    next
  end

  0.upto((n - (r * x)) / g) do |y|
    balls = r * x + g * y
    next if balls > n
    if balls == n
      ans += 1
      next
    end

    rest = n - balls
    ans += 1 if rest % b == 0
  end
end

puts ans