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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;

typedef pair<int, int> ii;
typedef tuple<int, int, int> iii;

typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<ld> vd;
typedef vector<ll> vl;

typedef set<int> si;
typedef set<ii> sii;
typedef set<ld> sd;
typedef set<ll> sl;

typedef map<int, int> mii;
typedef priority_queue<int> pqi;
typedef queue<int> qi;
 
#define mp make_pair
#define pb push_back
#define f first
#define s second

mt19937 rng((int) std::chrono::steady_clock::now().time_since_epoch().count());

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int r, g, b, n;
    cin >> r >> g >> b >> n;
    vi a = {r, g, b};
    vector<vl> dp(3, vl(n + 1, 0));
    dp[0][0] = 1;
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j <= n; j++) {
            if (i > 0) dp[i][j] += dp[i - 1][j];
            if (j - a[i] < 0) continue;
            dp[i][j] += dp[i][j - a[i]];
        }
    }

    cout << dp[2][n] << endl;
}

/*
USE LONG LONG!!!!

:pray: :fishy15:
:pray: :summitosity:
:pray: :prodakcin:

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   `//-.|  (  ,\\)\//\)\/_  ) |
   //___\   `\\\/\\/\/\\///'  /
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\       `-.  '_`.      .'_` \ ,-"~`/
 `.__.-'`/   (-\        /-) |-.__,'
   ||   |     \O)  /^\ (O/  | .        <-  BESSIE THE COW
   `\\  |         /   `\    /
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      `\\ `-.  /' .---.--.\
        `\\/`~(, '()      ('
         /(O) \\   _,.-.,_)    
        //  \\ `\'`      /
       / |  ||   `""""~"`
     /'  |__||
           `o
*/