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 Ruby (2.3.3) (judge verdict: Accepted)

R, G, B, N = gets.strip.split(/ /).collect(&:to_i)

$cache = []
def countGB(n)
	if count = $cache[n]
		return count
	end
	x = 0
	count = 0
	while x <= n
		if (n - x) % B == 0
			count += 1
		end
		x += G
	end
	
	$cache[n] = count
end

x = 0
count = 0
while x <= N
	count += countGB(N - x)
	x += R
end

puts count