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
$input = explode(' ', trim(fgets(STDIN)));

$r = (int)$input[0];
$g = (int)$input[1];
$b = (int)$input[2];
$n = (int)$input[3];

$r_max = (int)floor($n / $r);
$g_max = (int)floor($n / $g);
$b_max = (int)floor($n / $b);

$cnt = 0;
for ($rc=0; $rc <= $r_max; $rc++) { 
	for ($gc=0; $gc <= $g_max; $gc++) { 
		if (($n - $rc * $r - $gc * $g) >= 0 && ($n - $rc * $r - $gc * $g)%$b === 0) {
			// echo $rc . ' ' . $gc . PHP_EOL;
			++$cnt;
		}
	}
}

echo $cnt;