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 Lua (5.3.2) (judge verdict: Accepted)

a, b, c, n = io.read("*n", "*n", "*n", "*n")
t = {}
for i = 1, n + 1 do
  t[i] = 0
end
-- f(x) * (1-x^a)(1-x^b)(1-x^c) = 1
t[1] = 1
for i = 2, n + 1 do
  v = 0
  if a < i then v = v - t[i - a] end
  if b < i then v = v - t[i - b] end
  if c < i then v = v - t[i - c] end
  if a + b < i then v = v + t[i - a - b] end
  if b + c < i then v = v + t[i - b - c] end
  if c + a < i then v = v + t[i - c - a] end
  if a + b + c < i then v = v - t[i - a - b - c] end
  t[i] = -v
end
print(t[n + 1])