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)

require 'pp'
r,g,b,n = gets.split.map(&:to_i)
# p [r,g,b,n]
bb = (0..(n / b)).to_a
# p bb
# puts
cnt = 0
(n / r + 1).times do |rr|
  (n / g + 1).times do |gg|
    # p [rr * r,gg*g]
    next if rr*r + gg*g >= n+1
    if x = bb.bsearch{|x| x*b >= n - (rr*r + gg*g)}
      cnt += 1 if x*b == n - (rr*r + gg*g)
    end
  end
end
p cnt
# 4 87058