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.chomp!.split(" ").map!(&:to_i)

box = {
    "R" => R,
    "G" => G,
    "B" => B,
}.sort {|(_, v1), (_, v2)| v2 <=> v1 }.to_h

max_r = N / R
max_g = N / G
max_b = N / B

# Rをr個選んだとき
memo = []
0.upto(max_r) do |i|
    memo[i] = [i, N - i * R]
end

memo2 = []
count = 0

0.upto(max_g) do |i|
    memo.each do |m|
        x = m[1] - i * G
        if x >= 0 && x % B == 0
            #memo2.push([memo[0][0], i, x])
            count += 1
            #puts "#{memo[0][0]},#{i}"
        end
    end
end

puts count

#require 'pp'
#pp memo2.count