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 PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php
fscanf(STDIN,"%d %d %d %d",$r,$g,$b,$n);
$count=0;
$warir=($n-$n%$r)/$r;
$warig=($n-$n%$r)/$g;
$warib=($n-$n%$r)/$b;
if($warir<$warig)$warimax=$warig;
if($warib>$warig)$warimax=$warib;


for($i=0;$i<=$warir;$i++){

  for($j=0;$j<=($n-$r*$i)/$g;$j++){

    for($k=0;$k<=($n-$r*$i-$g*$j)/$b;$k++){
     if($i*$r+$j*$g+$k*$b==$n){
       $count+=1;
       }
     }

   }

}
echo($count);
?>