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: Time Limit Exceeded)

def valid?(current, stride, n)
  return false if current > n
  diff = n - current
  diff % stride == 0
end

r, g, b, n = gets.split.map(&:to_i)
nums = [r, g, b]
nums.sort.reverse
maxes = nums.map do |num|
  ((n + num - 1) / num).to_i
end

ans = 0
count = 0
for i in 0..maxes[0]
  for j in 0..maxes[1]
    current = i * nums[0] + j * nums[1]
    if valid?(current, nums[2], n)
      ans += 1
    end
  end
end

puts ans