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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
list($x,$y,$z,$n)=explode(" ",trim(fgets(STDIN)));
$r=max($x,$y,$z);
$b=min($x,$y,$z);
$g=$x+$y+$z-$r-$b;
$ans=0;
$i=0;
while($i*$r<=$n){
  $j=0;
  while($j*$g<=$n-$i*$r){
    if(($n-$i*$r-$j*$g)%$b==0){
      ++$ans;
    }
    ++$j;
  }
  ++$i;
}
echo $ans;