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)

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 = nums.sort.reverse
maxes = nums.map do |num|
  ((n + num - 1) / num).to_i
end
ans = 0
count = 0
while count <= n
  rest = n - count
  c2 = 0
  valids = []
  while c2 <= rest && valids.length < 2
    if valid?(c2 + count, nums[2], n)
      valids << c2
    end
    c2 += nums[1]
  end
  if valids.length == 1
    ans += 1
  elsif valids.length == 2
    diff = valids[1] - valids[0]
    r = rest - valids[1]
    ans += 2
    ans += (r / diff)
  end
  count += nums[0]
end

puts ans