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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun solve (r g b n)
  (let ((ans 0))
    (loop :for ri :from 0 :to (floor (/ n r))
          :do
             (loop :for gi :from 0 :to (floor (/ (- n (* ri r)) g))
                   :do
                      (if (zerop (rem (- n (* ri r) (* gi g)) b))
                          (setf ans (1+ ans)))))
    ans))

(defun main ()
  (let ((r (read))
        (g (read))
        (b (read))
        (n (read)))
    (format t "~A~%" (solve r g b n))))

(main)