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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<stdint.h>
#include<inttypes.h>

typedef int32_t i32;

void trans (i32 a, i32 *dp, i32 n) {
  for (i32 i = a; i <= n; ++i) {
    dp[i] += dp[i - a];
  }
}

void run (void) {
  i32 a, b, c, n;
  scanf ("%" SCNi32 "%" SCNi32 "%" SCNi32 "%" SCNi32, &a, &b, &c, &n);
  i32 *dp = (i32 *) calloc (n + 1, sizeof (i32));
  dp[0] = 1;
  trans (a, dp, n);
  trans (b, dp, n);
  trans (c, dp, n);
  printf ("%" PRIi32 "\n", dp[n]);
}

int main (void) {
  run();
  return 0;
}