Problem:
Score : 700 points

Problem Statement

Takahashi has a tower which is divided into N layers.
Initially, all the layers are uncolored. Takahashi is going to paint some of the layers in red, green or blue to make a beautiful tower.
He defines the beauty of the tower as follows:

The beauty of the tower is the sum of the scores of the N layers, where the score of a layer is A if the layer is painted red, A+B if the layer is painted green, B if the layer is painted blue, and 0 if the layer is uncolored.

Here, A and B are positive integer constants given beforehand. Also note that a layer may not be painted in two or more colors.

Takahashi is planning to paint the tower so that the beauty of the tower becomes exactly K.
How many such ways are there to paint the tower? Find the count modulo 998244353.
Two ways to paint the tower are considered different when there exists a layer that is painted in different colors, or a layer that is painted in some color in one of the ways and not in the other.

Constraints

1 ≤ N ≤ 3×10^5

1 ≤ A,B ≤ 3×10^5

0 ≤ K ≤ 18×10^{10}

All values in the input are integers.

Input

Input is given from Standard Input in the following format:

N A B K

Output

Print the number of the ways to paint tiles, modulo 998244353.

Sample Input 1

4 1 2 5

Sample Output 1

40

In this case, a red layer worth 1 points, a green layer worth 3 points and the blue layer worth 2 points. The beauty of the tower is 5 when we have one of the following sets of painted layers:

1 green, 1 blue

1 red, 2 blues

2 reds, 1 green

3 reds, 1 blue

The total number of the ways to produce them is 40.

Sample Input 2

2 5 6 0

Sample Output 2

1

The beauty of the tower is 0 only when all the layers are uncolored. Thus, the answer is 1.

Sample Input 3

90081 33447 90629 6391049189

Sample Output 3

577742975

Solution in Rust (1.15.1) (judge verdict: Accepted)

// SNIPPET read
pub trait Readable {
    type Output;
    fn words_count() -> usize;
    fn read_words(words: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $t:ty, $words_count:expr, |$words:ident| $read_words:expr ) => {
        impl Readable for $t {
            type Output = $t;
            fn words_count() -> usize { $words_count }
            fn read_words($words: &[&str]) -> Result<$t, String> {
                Ok($read_words)
            }
        }
    };
}
readable!((), 1, |_ss| ());
readable!(String, 1, |ss| ss[0].to_string());
impl Readable for char {
    type Output = char;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<char, String> {
        let chars: Vec<char> = words[0].chars().collect();
        if chars.len() == 1 {
            Ok(chars[0])
        } else {
            Err(format!("cannot parse `{}` as a char", words[0]))
        }
    }
}
pub struct Chars();
impl Readable for Chars {
    type Output = Vec<char>;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Vec<char>, String> {
        Ok(words[0].chars().collect())
    }
}
macro_rules! impl_readable_for_ints {
    ( $( $t:ty )* ) => { $(
        impl Readable for $t {
            type Output = Self;
            fn words_count() -> usize { 1 }
            fn read_words(words: &[&str]) -> Result<$t, String> {
                use std::str::FromStr;
                <$t>::from_str(words[0]).map_err(|_| {
                    format!("cannot parse `{}` as {}", words[0], stringify!($t))
                })
            }
        }
    )* };
}
impl_readable_for_ints!(i8 u8 i16 u16 i32 u32 i64 u64 isize usize f32 f64);
macro_rules! define_one_origin_int_types {
    ( $new_t:ident $int_t:ty ) => {
        #[allow(non_camel_case_types)]
        pub struct $new_t;
        impl Readable for $new_t {
            type Output = $int_t;
            fn words_count() -> usize { 1 }
            fn read_words(words: &[&str]) -> Result<Self::Output, String> {
                <$int_t>::read_words(words).map(|n| n-1)
            }
        }
    };
    ( $new_t:ident $int_t:ty; $( $inner_new_t:ident $inner_int_t:ty );* ) => {
        define_one_origin_int_types!($new_t $int_t);
        define_one_origin_int_types!($($inner_new_t $inner_int_t);*);
    };
}
define_one_origin_int_types!(u8_ u8; u16_ u16; u32_ u32; u64_ u64; usize_ usize);
macro_rules! impl_readable_for_tuples {
    ( $t:ident $var:ident ) => ();
    ( $t:ident $var:ident; $( $inner_t:ident $inner_var:ident );* ) => {
        impl_readable_for_tuples!($($inner_t $inner_var);*);
        impl<$t: Readable, $($inner_t: Readable),*> Readable
            for ($t, $($inner_t),*)
        {
            type Output = ( <$t>::Output, $(<$inner_t>::Output),* );
            fn words_count() -> usize {
                let mut n = <$t>::words_count();
                $(
                    n += <$inner_t>::words_count();
                )*
                n
            }
            #[allow(unused_assignments)]
            fn read_words(words: &[&str]) ->
                Result<Self::Output, String>
            {
                let mut start = 0;
                let $var = <$t>::read_words(
                    &words[start .. start+<$t>::words_count()]
                )?;
                start += <$t>::words_count();
                $(
                    let $inner_var =
                        <$inner_t>::read_words(
                            &words[start .. start+<$inner_t>::words_count()]
                        )?;
                    start += <$inner_t>::words_count();
                )*
                Ok(( $var, $($inner_var),* ))
            }
        }
    };
}
impl_readable_for_tuples!(T8 x8; T7 x7; T6 x6; T5 x5; T4 x4; T3 x3; T2 x2; T1 x1);
pub trait ReadableFromLine {
    type Output;
    fn read_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_words(line: &str) -> Vec<&str> {
    #[allow(deprecated)]
    line.trim_right_matches('\n').split_whitespace().collect()
}
impl<T: Readable> ReadableFromLine for T {
    type Output = T::Output;
    fn read_line(line: &str) -> Result<T::Output, String> {
        let words = split_into_words(line);
        if words.len() != T::words_count() {
            return Err(format!("line `{}` has {} words, expected {}",
                               line, words.len(), T::words_count()));
        }
        T::read_words(&words)
    }
}
macro_rules! impl_readable_from_line_for_tuples_with_from_iterator {
    ( $u:ident : $( + $bound:path )* => $seq_in:ty, $seq_out:ty; $t:ident $var:ident ) => {
        impl<$u: Readable> ReadableFromLine for $seq_in
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = $seq_out;
            fn read_line(line: &str) -> Result<$seq_out, String> {
                let n = $u::words_count();
                let words = split_into_words(line);
                if words.len() % n != 0 {
                    return Err(format!("line `{}` has {} words, expected multiple of {}",
                                       line, words.len(), n));
                }
                let mut result = Vec::new();
                for chunk in words.chunks(n) {
                    match $u::read_words(chunk) {
                        Ok(v) => result.push(v),
                        Err(msg) => {
                            let flagment_msg = if n == 1 {
                                format!("word {}", result.len())
                            } else {
                                let l = result.len();
                                format!("words {}-{}", n*l + 1, (n+1) * l)
                            };
                            return Err(format!(
                                "{} of line `{}`: {}", flagment_msg, line, msg
                            ));
                        }
                    }
                }
                Ok(result.into_iter().collect())
            }
        }
        impl<T: Readable, $u: Readable> ReadableFromLine for (T, $seq_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T::Output, $seq_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let n = T::words_count();
                #[allow(deprecated)]
                let trimmed = line.trim_right_matches('\n');
                let words_and_rest: Vec<&str> = trimmed.splitn(n + 1, ' ').collect();
                if words_and_rest.len() < n {
                    return Err(format!("line `{}` has {} words, expected at least {}",
                                       line, words_and_rest.len(), n));
                }
                let words = &words_and_rest[..n];
                let empty_str = "";
                let rest = words_and_rest.get(n).unwrap_or(&empty_str);
                Ok((T::read_words(words)?, <$seq_in>::read_line(rest)?))
            }
        }
    };
    ( $u:ident : $( + $bound:path )* => $seq_in:ty, $seq_out:ty;
      $t:ident $var:ident, $( $inner_t:ident $inner_var:ident ),+ ) => {
        impl_readable_from_line_for_tuples_with_from_iterator!(
            $u: $(+ $bound)* => $seq_in, $seq_out; $($inner_t $inner_var),+
        );
        impl<$t: Readable, $($inner_t: Readable),+ , $u: Readable> ReadableFromLine
            for ($t, $($inner_t),+ , $seq_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = ($t::Output, $($inner_t::Output),+ , $seq_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let mut n = $t::words_count();
                $(
                    n += $inner_t::words_count();
                )+
                #[allow(deprecated)]
                let trimmed = line.trim_right_matches('\n');
                let words_and_rest: Vec<&str> = trimmed.splitn(n + 1, ' ')
                    .collect();
                if words_and_rest.len() < n {
                    return Err(
                        format!("line `{}` has {} words, expected at least {}",
                                line, words_and_rest.len(), n)
                    );
                }
                let words = &words_and_rest[..n];
                let empty_str = "";
                let rest = words_and_rest.get(n).unwrap_or(&empty_str);
                let ($var, $($inner_var),*) =
                    <($t, $($inner_t),+)>::read_words(words)?;
                Ok(($var, $($inner_var),* , <$seq_in>::read_line(rest)?))
            }
        }
    };
}
#[macro_export]
macro_rules! readable_collection {
    ($u:ident => $collection_in:ty, $collection_out:ty) => {
        impl_readable_from_line_for_tuples_with_from_iterator!(
            $u: => $collection_in, $collection_out;
            T8 x8, T7 x7, T6 x6, T5 x5, T4 x4, T3 x3, T2 x2, T1 x1
        );
    };
    ($u:ident : $( $bound:path ),* => $collection_in:ty, $collection_out:ty) => {
        impl_readable_from_line_for_tuples_with_from_iterator!(
            $u: $(+ $bound)* => $collection_in, $collection_out;
            T8 x8, T7 x7, T6 x6, T5 x5, T4 x4, T3 x3, T2 x2, T1 x1
        );
    }
}
readable_collection!(U => Vec<U>, Vec<U::Output>);
readable_collection!(
    U => std::collections::VecDeque<U>, std::collections::VecDeque<U::Output>
);
readable_collection!(
    U: Eq, std::hash::Hash => std::collections::HashSet<U>, std::collections::HashSet<U::Output>
);
readable_collection!(
    U: Ord => std::collections::BTreeSet<U>, std::collections::BTreeSet<U::Output>
);
readable_collection!(
    U: Ord => std::collections::BinaryHeap<U>, std::collections::BinaryHeap<U::Output>
);
pub fn read<T: ReadableFromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::read_line(&line).unwrap()
}
#[macro_export]
macro_rules! read {
    () => {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
    };
    ( $pat:pat = $t:ty ) => {
        let $pat = read::<$t>();
    };
    ( $( $pat:pat = $t:ty ),+ ) => {
        read!(($($pat),*) = ($($t),*));
    };
}
#[macro_export]
macro_rules! readls {
    ( $( $pat:pat = $t:ty ),+ ) => {
        $(
            read!($pat = $t);
        )*
    };
}
pub fn readx<T: ReadableFromLine>() -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result = stdin.lock().lines().map(|line_result| {
        let line = line_result.expect("read from stdin failed");
        T::read_line(&line).unwrap()
    }).collect();
    result
}
#[macro_export]
macro_rules! readx_loop {
    ( |$pat:pat = $t:ty| $body:expr ) => {
        {
            use std::io::BufRead;
            let stdin = std::io::stdin();
            for line in stdin.lock().lines() {
                let line = line.expect("read from stdin failed");
                let $pat = <$t>::read_line(&line).unwrap();
                $body
            }
        }
    };
    ( |$($pat:pat = $t:ty),*| $body:expr ) => {
        readx_loop!(|($($pat),*) = ($($t),*)| $body);
    };
}
pub fn readn<T: ReadableFromLine>(n: usize) -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result: Vec<T::Output> = stdin.lock().lines().take(n).map(|line_result| {
        let line = line_result.expect("read from stdin failed");
        T::read_line(&line).unwrap()
    }).collect();
    if result.len() < n {
        panic!("expected reading {} lines, but only {} lines are read",
               n, result.len());
    }
    result
}
#[macro_export]
macro_rules! readn_loop {
    ( $n:expr, |$pat:pat = $t:ty| $body:expr ) => {
        {
            use std::io::BufRead;
            let stdin = std::io::stdin();
            let mut lock = stdin.lock();
            for _ in 0..$n {
                let mut line = String::new();
                lock.read_line(&mut line).expect("read from stdin failed");
                let $pat = <$t>::read_line(&line).unwrap();
                $body
            }
        }
    };
    ( $n:expr, |$($pat:pat = $t:ty),*| $body:expr ) => {
        readn_loop!($n, |($($pat),*) = ($($t),*)| $body);
    };
}
pub trait Words {
    fn read<T: Readable>(&self) -> T::Output;
}
impl<'a> Words for [&'a str] {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(self).unwrap()
    }
}
impl<'a> Words for &'a str {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(&[self]).unwrap()
    }
}
// SNIPPET iter
#[derive(Clone)]
pub struct StepBy<I> {
    iter: I,
    step: usize,
    first_take: bool
}
impl<I: Iterator> Iterator for StepBy<I> {
    type Item = I::Item;
    fn next(&mut self) -> Option<Self::Item> {
        if self.first_take {
            self.first_take = false;
            self.iter.next()
        } else {
            self.iter.nth(self.step)
        }
    }
}
pub struct Chunks<I: Iterator> {
    iter: I,
    size: usize
}
impl<I: Iterator> Iterator for Chunks<I> {
    type Item = Vec<I::Item>;
    fn next(&mut self) -> Option<Self::Item> {
        let first = self.iter.next();
        if first.is_none() {
            return None;
        }
        let mut chunk = Vec::with_capacity(self.size);
        chunk.push(first.unwrap());
        for _ in 0..self.size-1 {
            match self.iter.next() {
                Some(x) => chunk.push(x),
                None => break
            }
        }
        Some(chunk)
    }
}
#[derive(Clone)]
pub struct LScan<I: Iterator, S: Clone, F: FnMut(&S, I::Item) -> S> {
    iter: I,
    state: Option<S>,
    f: F,
}
impl<I: Iterator, S: Clone, F> Iterator for LScan<I, S, F>
where
    F: FnMut(&S, I::Item) -> S,
{
    type Item = S;
    fn next(&mut self) -> Option<S> {
        if self.state.is_none() {
            return None;
        }
        let state_inner = self.state.take().unwrap();
        if let Some(item) = self.iter.next() {
            self.state = Some((self.f)(&state_inner, item));
        }
        Some(state_inner)
    }
}
pub struct Flatten<I: Iterator>
where
    I::Item: IntoIterator
{
    outer_iter: I,
    inner_iter: Option<<<I as Iterator>::Item as IntoIterator>::IntoIter>
}
impl<I, J> Iterator for Flatten<I>
where
    I: Iterator<Item = J>,
    J: IntoIterator
{
    type Item = <<J as IntoIterator>::IntoIter as Iterator>::Item;
    fn next(&mut self) -> Option<J::Item> {
        loop {
            if let Some(inner_iter) = self.inner_iter.as_mut() {
                if let item@Some(_) = inner_iter.next() {
                    return item
                }
            }
            match self.outer_iter.next() {
                None => return None,
                Some(inner) => self.inner_iter = Some(inner.into_iter())
            }
        }
    }
}
/*
impl<I, J> DoubleEndedIterator for Flatten<I>
where
    I: DoubleEndedIterator,
    J: DoubleEndedIterator,
    I::Item: J {}
*/
pub struct GroupBy<K: Eq, I: Iterator, F: FnMut(&I::Item) -> K> {
    cur: Option<(I::Item, K)>,
    iter: I,
    key_fn: F
}
impl<K: Eq, I: Iterator, F: FnMut(&I::Item) -> K> Iterator for GroupBy<K, I, F> {
    type Item = (K, Vec<I::Item>);
    fn next(&mut self) -> Option<(K, Vec<I::Item>)> {
        let cur = self.cur.take();
        cur.map(|(item, key)| {
            let mut group = vec![item];
            loop {
                let next = self.iter.next();
                match next {
                    Some(next_item) => {
                        let next_key = (self.key_fn)(&next_item);
                        if key == next_key {
                            group.push(next_item);
                        } else {
                            self.cur = Some((next_item, next_key));
                            break;
                        }
                    }
                    None => {
                        self.cur = None;
                        break;
                    }
                }
            }
            (key, group)
        })
    }
}
pub struct RunLength<I: Iterator> {
    cur: Option<I::Item>,
    iter: I
}
impl<I: Iterator> Iterator for RunLength<I> where I::Item: Eq {
    type Item = (I::Item, usize);
    fn next(&mut self) -> Option<(I::Item, usize)> {
        let cur = self.cur.take();
        cur.map(|value| {
            let mut length = 1;
            loop {
                let next = self.iter.next();
                match next {
                    Some(next_value) => {
                        if value == next_value {
                            length += 1;
                        } else {
                            self.cur = Some(next_value);
                            break;
                        }
                    }
                    None => {
                        self.cur = None;
                        break;
                    }
                }
            }
            (value, length)
        })
    }
}
pub trait IteratorExt: Iterator {
    fn step_by_(self, step: usize) -> StepBy<Self> where Self: Sized {
        assert_ne!(step, 0);
        StepBy {
            iter: self,
            step: step - 1,
            first_take: true
        }
    }
    fn for_each<F: FnMut(Self::Item)>(self, mut f: F) where Self: Sized {
        for item in self {
            f(item);
        }
    }
    fn chunks(self, size: usize) -> Chunks<Self> where Self: Sized {
        assert!(size > 0);
        Chunks {
            iter: self,
            size: size
        }
    }
    fn lscan<S: Clone, F>(self, state: S, f: F) -> LScan<Self, S, F>
    where
        Self: Sized,
        F: FnMut(&S, Self::Item) -> S,
    {
        LScan {
            iter: self,
            state: Some(state),
            f: f,
        }
    }
    fn get_unique(mut self) -> Option<Self::Item> where Self: Sized, Self::Item: Eq {
        let first_opt = self.next();
        first_opt.and_then(|first| {
            if self.all(|item| item == first) { Some(first) } else { None }
        })
    }
    fn flatten(mut self) -> Flatten<Self> where Self: Sized, Self::Item: IntoIterator {
        let inner_opt = self.next();
        Flatten {
            outer_iter: self,
            inner_iter: inner_opt.map(|inner| inner.into_iter())
        }
    }
    fn group_by<K: Eq, F: FnMut(&Self::Item) -> K>(mut self, mut f: F) -> GroupBy<K, Self, F> where Self: Sized {
        let next = self.next();
        GroupBy {
            cur: next.map(|item| {
                let key = f(&item);
                (item, key)
            }),
            iter: self,
            key_fn: f
        }
    }
    fn run_length(mut self) -> RunLength<Self> where Self: Sized, Self::Item: Eq {
        RunLength {
            cur: self.next(),
            iter: self
        }
    }
    fn join<T: std::fmt::Display>(mut self, sep: T) -> String
    where
        Self: Sized, Self::Item: std::fmt::Display
    {
        let mut result = String::new();
        if let Some(first) = self.next() {
            result.push_str(&format!("{}", first));
        }
        for s in self {
            result.push_str(&format!("{}{}", sep, s));
        }
        result
    }
    fn cat(self) -> String where Self: Sized, Self::Item: std::fmt::Display { self.join("") }
}
impl<I: Iterator> IteratorExt for I {}
pub struct Unfold<T, F> where F: FnMut(&T) -> Option<T> {
    state: Option<T>,
    f: F
}
impl<T, F> Iterator for Unfold<T, F> where F: FnMut(&T) -> Option<T> {
    type Item = T;
    fn next(&mut self) -> Option<T> {
        if self.state.is_none() {
            return None;
        }
        let state_inner = self.state.take().unwrap();
        self.state = (self.f)(&state_inner);
        Some(state_inner)
    }
}
pub fn unfold<T, F>(init: T, f: F) -> Unfold<T, F> where F: FnMut(&T) -> Option<T> {
    Unfold { state: Some(init), f: f }
}
pub struct Iterate<T, F> where F: FnMut(&T) -> T {
    state: T,
    f: F
}
impl<T, F> Iterator for Iterate<T, F> where F: FnMut(&T) -> T {
    type Item = T;
    fn next(&mut self) -> Option<T> {
        use std::mem::swap;
        let mut state = (self.f)(&self.state);
        swap(&mut state, &mut self.state);
        Some(state)
    }
}
pub fn iterate<T, F>(init: T, f: F) -> Iterate<T, F>
where
    F: FnMut(&T) -> T,
{
    Iterate { state: init, f: f }
}
// SNIPPET modp
pub type ModPBase = u64;
pub type ModPModulus = u32;
static mut MODULUS: ModPBase = 0;
#[derive(Clone, Copy, PartialEq, Eq)]
pub struct ModP {
    base: ModPBase
}
impl ModP {
    pub unsafe fn set_mod(modulus: ModPModulus) -> Result<(), String> {
        if modulus <= 1 {
            return Err(format!("{} is not a prime number.", modulus));
        }
        if modulus >= 4 {
            if modulus % 2 == 0 || modulus % 3 == 0 {
                return Err(format!("{} is not a prime number.", modulus));
            }
            let mut divisor = 5;
            loop {
                if divisor * divisor > modulus {
                    break;
                }
                if modulus % divisor == 0 {
                    return Err(format!("{} is not a prime number.", modulus));
                }
                divisor += 2;
                if divisor * divisor > modulus {
                    break;
                }
                if modulus % divisor == 0 {
                    return Err(format!("{} is not a prime number.", modulus));
                }
                divisor += 4;
            }
        }
        MODULUS = modulus as ModPBase;
        Ok(())
    }
    pub fn new(n: ModPBase) -> ModP {
        if !cfg!(test) {
            assert!(unsafe { MODULUS } != 0,
                    "Call ModP::set_mod before using ModP.");
        }
        ModP { base: n % unsafe { MODULUS } }
    }
    pub unsafe fn new_unchecked(n: ModPBase) -> ModP {
        ModP { base: n }
    }
    pub fn base(&self) -> ModPBase {
        self.base
    }
    pub fn pow(self, exp: ModPBase) -> ModP {
        if exp == 0 { ModP::new(1) } else {
            let sub = self.pow(exp / 2);
            if exp % 2 == 0 {
                sub * sub
            } else {
                self * sub * sub
            }
        }
    }
    pub fn inv(self) -> ModP {
        assert!(self.base() != 0);
        self.pow(unsafe { MODULUS } - 2)
    }
}
pub fn modp(x: ModPBase) -> ModP {
    ModP::new(x)
}
impl std::fmt::Display for ModP {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.base())
    }
}
impl std::fmt::Debug for ModP {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{} mod P", self.base())
    }
}
impl PartialEq<ModPBase> for ModP {
    fn eq(&self, other: &ModPBase) -> bool {
        self.base() == other % unsafe { MODULUS }
    }
}
impl PartialEq<ModP> for ModPBase {
    fn eq(&self, other: &ModP) -> bool {
        self % unsafe { MODULUS } == other.base() % unsafe { MODULUS }
    }
}
impl std::ops::Add for ModP {
    type Output = ModP;
    fn add(self, rhs: ModP) -> ModP {
        let m = unsafe { MODULUS };
        ModP { base: (self.base() + rhs.base() % m) % m }
    }
}
impl std::ops::Add<ModPBase> for ModP {
    type Output = ModP;
    fn add(self, rhs: ModPBase) -> ModP {
        self + ModP::new(rhs)
    }
}
impl std::ops::Add<ModP> for ModPBase {
    type Output = ModP;
    fn add(self, rhs: ModP) -> ModP {
        ModP::new(self) + rhs.base()
    }
}
impl std::ops::AddAssign for ModP {
    fn add_assign(&mut self, rhs: ModP) {
        *self = *self + rhs
    }
}
impl std::ops::AddAssign<ModPBase> for ModP {
    fn add_assign(&mut self, rhs: ModPBase) {
        *self = *self + ModP::new(rhs)
    }
}
impl std::ops::Neg for ModP {
    type Output = ModP;
    fn neg(self) -> ModP {
        ModP::new(unsafe { MODULUS } - self.base())
    }
}
impl std::ops::Sub for ModP {
    type Output = ModP;
    fn sub(self, rhs: ModP) -> ModP {
        self + (-rhs)
    }
}
impl std::ops::Sub<ModPBase> for ModP {
    type Output = ModP;
    fn sub(self, rhs: ModPBase) -> ModP {
        self - ModP::new(rhs)
    }
}
impl std::ops::Sub<ModP> for ModPBase {
    type Output = ModP;
    fn sub(self, rhs: ModP) -> ModP {
        ModP::new(self) - rhs
    }
}
impl std::ops::SubAssign for ModP {
    fn sub_assign(&mut self, rhs: ModP) {
        *self = *self - rhs;
    }
}
impl std::ops::SubAssign<ModPBase> for ModP {
    fn sub_assign(&mut self, rhs: ModPBase) {
        *self = *self - ModP::new(rhs)
    }
}
impl std::ops::Mul for ModP {
    type Output = ModP;
    fn mul(self, rhs: ModP) -> ModP {
        let m = unsafe { MODULUS };
        ModP { base: self.base() * (rhs.base() % m) % m }
    }
}
impl std::ops::Mul<ModPBase> for ModP {
    type Output = ModP;
    fn mul(self, rhs: ModPBase) -> ModP {
        self * ModP::new(rhs)
    }
}
impl std::ops::Mul<ModP> for ModPBase {
    type Output = ModP;
    fn mul(self, rhs: ModP) -> ModP {
        ModP::new(self) * rhs.base()
    }
}
impl std::ops::MulAssign for ModP {
    fn mul_assign(&mut self, rhs: ModP) {
        *self = *self * rhs
    }
}
impl std::ops::MulAssign<ModPBase> for ModP {
    fn mul_assign(&mut self, rhs: ModPBase) {
        *self = *self * ModP::new(rhs)
    }
}
impl std::ops::Div for ModP {
    type Output = ModP;
    fn div(self, rhs: ModP) -> ModP {
        self * rhs.inv()
    }
}
impl std::ops::Div<ModPBase> for ModP {
    type Output = ModP;
    fn div(self, rhs: ModPBase) -> ModP {
        self * ModP::new(rhs).inv()
    }
}
impl std::ops::Div<ModP> for ModPBase {
    type Output = ModP;
    fn div(self, rhs: ModP) -> ModP {
        ModP::new(self) * rhs.inv()
    }
}
impl std::ops::DivAssign for ModP {
    fn div_assign(&mut self, rhs: ModP) {
        *self = *self / rhs;
    }
}
impl std::ops::DivAssign<ModPBase> for ModP {
    fn div_assign(&mut self, rhs: ModPBase) {
        *self = *self / ModP::new(rhs)
    }
}
impl std::iter::Sum for ModP {
    fn sum<I: Iterator<Item=ModP>>(iter: I) -> ModP {
        let mut ans = 0;
        for n in iter {
            ans += n.base();
        }
        ModP::new(ans)
    }
}
impl<'a> std::iter::Sum<&'a ModP> for ModP {
    fn sum<I: Iterator<Item=&'a ModP>>(iter: I) -> ModP {
        let mut ans = 0;
        for n in iter {
            ans += n.base();
        }
        ModP::new(ans)
    }
}
impl std::iter::Product for ModP {
    fn product<I: Iterator<Item=ModP>>(iter: I) -> ModP {
        let mut ans = unsafe { ModP::new_unchecked(1) };
        for n in iter {
            ans *= n;
        }
        ans
    }
}
impl<'a> std::iter::Product<&'a ModP> for ModP {
    fn product<I: Iterator<Item=&'a ModP>>(iter: I) -> ModP {
        let mut ans = unsafe { ModP::new_unchecked(1) };
        for &n in iter {
            ans *= n;
        }
        ans
    }
}
readable!(ModP, 1, |ws| ModP::new(ws[0].read::<ModPBase>()));
// END SNIPPETS

fn choose(n: u64, m: u64, fs: &[ModP]) -> ModP {
    fs[n as usize] / (fs[(n-m) as usize] * fs[m as usize])
}

fn calc(a: u64, b: u64, n: u64, fs: &[ModP]) -> ModP {
    choose(n, a, fs) * choose(n, b, fs)
}

fn main() {
    unsafe { ModP::set_mod(998244353).unwrap(); }
    read!(n = u64, a = u64, b = u64, k = u64);
    let fs: Vec<ModP> = (1..n+1).lscan(modp(1), |&acc, i| acc * i).collect();
    let ans: ModP = (0..n+1).map(|i_a| {
        k.checked_sub(i_a * a).map_or(modp(0), |rest| {
            if rest % b != 0 {
                return modp(0);
            }
            let i_b = rest / b;
            if i_b > n { modp(0) } else { calc(i_a, i_b, n, &fs) }
        })
    }).sum();
    println!("{}", ans);
}