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 Python (3.4.3) (judge verdict: Accepted)

import collections
import itertools
r,g,b,n=map(int,input().split())
x,y=n//r,n//g
x,y=list(range(0,r*x+1,r)),list(range(0,g*y+1,g))
l=[i+j for i,j in itertools.product(x,y) if i+j<=n]
z=collections.Counter(l)
count=0
for key,value in zip(z.keys(),z.values()):
  v=n-key
  if v==0:
    count+=value
  elif v%b==0:
    count+=value
print(count)