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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

function main(input){
  const lines = input.split('\n');
  const R = lines[0].split(' ').map(x => parseInt(x))[0];
  const G = lines[0].split(' ').map(x => parseInt(x))[1];
  const B = lines[0].split(' ').map(x => parseInt(x))[2];
  const N = lines[0].split(' ').map(x => parseInt(x))[3];

  var result = 0;
  const R_limit=Math.max(Math.ceil(N/R),1);
  const G_limit=Math.max(Math.ceil(N/G),1);
  const B_limit=Math.max(Math.ceil(N/B),1);
  for(var r=0;r<=R_limit;r++){
    if(r*R>N){break;}
    for(var g=0;g<=G_limit;g++){
      if(g*G>N){break;}
      for(var b=0;b<=B_limit;b++){
        if(b*B>N){break;}
        if(r*R + g*G + b*B < N){ b=Math.floor( (N-(r*R + g*G))/B ); }
        if(r*R + g*G + b*B==N){result++;}
      }
    }
  }

  console.log(result);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));