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 LuaJIT (2.0.4) (judge verdict: Accepted)

local ior = io.input()
local r, g, b, n = ior:read("*n", "*n", "*n", "*n")
local cnt = 0
for i = 0, n do
  for j = 0, n - i do
    local k = n - i - j
    if i % r == 0 and j % g == 0 and k % b == 0 then cnt = cnt + 1 end
  end
end
print(cnt)