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)

# https://atcoder.jp/contests/diverta2019/tasks/diverta2019_b

r, g, b, n = gets.split.map(&:to_i)
# dp[r][g][b] = sum
dp = Array.new(3000).map { Array.new(3000) }.map { Array.new(3000) }

res = 0

0.upto(n / r) do |i|
  break if i * r > n
  0.upto(n / g) do |j|
    rest = n - (i * r + j * g)
    break if rest < 0
    res += 1 if rest % b == 0
  end
end

puts res