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: Time Limit Exceeded)

r,g,b,n = map(int,input().split())
sorted_rgb = sorted((r,g,b))
import itertools
cnt = 0
for x in itertools.product([i for i in range(int(n/sorted_rgb[0])+1)],[j for j in range(int(n/sorted_rgb[1])+1)]):
    if ((n-x[0]*sorted_rgb[0]-x[1]*sorted_rgb[1])%sorted_rgb[2] == 0)&((n-x[0]*sorted_rgb[0]-x[1]*sorted_rgb[1])>=0):
        cnt +=1
print(cnt)