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)

local R,G,B,N = io.read("n", "n", "n", "n")

local cnt = 0
for r=0,N do
    local lim = (N - R*r) / G
    --print(lim)
    for g=0,lim do
        local b = (N - R*r - G*g) / B
        if b >= 0 and b == math.floor(b) then
            cnt = cnt + 1
            --print(r,g,b)
        end
    end
end
print(cnt)