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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]

#[macro_use]
mod _input {
    use std::fmt;
    use std::io::{self, Read};
    use std::str::{self, FromStr};

    macro_rules! input {
        ($($name:ident : $t:tt),*,) => {
            input!($($name: $t),*)
        };
        ($($name:ident : $t:tt),*) => {
            let mut _scanned = ::_input::Scanned::new(::std::io::stdin(), 1024);
            $(
                let $name = unsafe { _read_value!(_scanned, $t) };
            )*
        };
    }

    macro_rules! _read_value {
        ($scanned:expr, ($($t:tt),*)) => {
            ($(_read_value!($scanned, $t)),*)
        };
        ($scanned:expr, [$t:tt; $n:expr]) => {
            (0..$n).map(|_| _read_value!($scanned, $t)).collect::<Vec<_>>()
        };
        ($scanned:expr, _bytes) => {
            _read_value!($scanned, String).into_bytes()
        };
        ($scanned:expr, _1based) => {
            _read_value!($scanned, usize) - 1
        };
        ($scanned:expr, $t:ty) => {
            $scanned.next::<$t>()
        };
    }

    pub struct Scanned {
        buf: Vec<u8>,
        pos: usize,
    }

    impl Scanned {
        pub fn new<R: Read>(mut input: R, estimated: usize) -> Self {
            let mut buf_ = Vec::with_capacity(estimated);
            let _ = io::copy(&mut input, &mut buf_).unwrap();
            debug_assert!(str::from_utf8(&buf_).is_ok());
            debug_assert!(buf_.iter().all(|&c| u32::from(c) <= 0x7F));
            Scanned { buf: buf_, pos: 0 }
        }

        #[inline]
        pub unsafe fn next<T: FromStr>(&mut self) -> T
        where
            T::Err: fmt::Debug,
        {
            let mut start = None;
            loop {
                match (self.buf[self.pos], start.is_some()) {
                    (b' ', true) | (b'\n', true) => break,
                    (_, true) | (b' ', false) | (b'\n', false) => self.pos += 1,
                    (_, false) => start = Some(self.pos),
                }
            }
            let target = &self.buf[start.unwrap()..self.pos];
            str::from_utf8_unchecked(target).parse().unwrap()
        }
    }
}

use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::{self, BufWriter, Read, Stderr, StderrLock, Stdout, StdoutLock, Write};
use std::iter::{self, Product, Sum};
use std::num::{ParseFloatError, ParseIntError};
use std::ops::{
    Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Deref,
    DerefMut, Div, DivAssign, Mul, MulAssign, Neg, Not, Rem, RemAssign, Sub, SubAssign,
};
use std::str::{self, FromStr};
use std::{char, cmp, f32, f64, fmt, i16, i32, i64, i8, mem, thread, u16, u32, u64, u8};

fn main() {
    input! {
        r: u64,
        g: u64,
        b: u64,
        n: u64,
    }
    let mut a = 0;
    for s in 0..n / b + 1 {
        for t in 0..n / g + 1 {
            let k = b * s + g * t;
            if n >= k && (n - k) % r == 0 {
                a += 1;
            }
        }
    }
    println!("{}", a);
}