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)
# p R, G, B, N
MAX = 3000
# cnt = 0
# (N/R + 1).times do |r|
#   rest = N - r * R
#   p "rest = #{rest}"
#   (rest / G + 1).times do |g|
#     rest2 = rest - g * G
#     if rest % B == 0
#       p [r, g, rest / B]
#       cnt += 1
#     end
#   end
# end

cnt = 0
(0..MAX).each do |r|
  break if R*r > N
  (0..MAX).each do |g|
    break if R*r + G*g > N
    rest = N - (R*r+G*g)
    if rest % B == 0
      cnt += 1
      # p(r: r, g: g, b: (rest/B), rest: rest, R: R*r, G: G*g, N: N, RG: R*r+G*g, RGN: N - R*r+G*g)
    end
  end
end

puts cnt