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())
colors = [R, G, B]
colors.sort()
ans = 0

for c1 in range(N//colors[2]+1, -1, -1):
    C1 = c1*colors[2] 
    for c2 in range(N//colors[1], -1, -1):
        C2 = c2*colors[1] 
        C3 = (N-C1-C2)/colors[0]
        if C3 >= 0 and C3.is_integer():
            ans += 1

print(ans)