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

#include <bits/stdc++.h>
using namespace std;

//////////////////////////////   Begin Macros

#define all(x) (x).begin(), (x).end()
#define rep(i, N) for (int i = 0; i < (int)(N); i++)
#define reprev(i, N) for (int i = (int)(N)-1; i >= 0; i--)
#define rep1(i, N) for (int i = 1; i <= (int)(N); i++)
#define rep1rev(i, N) for (int i = (int)(N); i >= 0; i--)
#define forbe(i, b, e) for (int i = (b); i < (e); i++)
#define forberev(i, b, e) for (int i = (e)-1; i >= (b); i--)
#define forfl(i, f, l) for (int i = (f); i <= (l); i++)
#define forflrev(i, f, l) for (int i = (l); i >= (f); i--)
using ll = long long int;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
bool chmax(T &m, const T q)
{
  if (m < q)
  {
    m = q;
    return true;
  }
  else
    return false;
}
template <typename T>
bool chmin(T &m, const T q)
{
  if (m > q)
  {
    m = q;
    return true;
  }
  else
    return false;
}
template <typename T1, typename T2>
pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return {l.first + r.first, l.second + r.second}; }
template <typename T1, typename T2>
pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return {l.first - r.first, l.second - r.second}; }
template <typename T>
pair<T, T> operator*(const pair<T, T> &l, const T &r) { return {l.first * r, l.second * r}; }
template <typename T>
pair<T, T> operator/(const pair<T, T> &l, const T &r) { return {l.first / r, l.second / r}; }
template <typename T>
istream &operator>>(istream &is, vector<T> &vec)
{
  for (auto &v : vec)
    is >> v;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec)
{
  os << "[";
  for (auto v : vec)
    os << v << ",";
  os << "]";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const deque<T> &vec)
{
  os << "deq[";
  for (auto v : vec)
    os << v << ",";
  os << "]";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &vec)
{
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &vec)
{
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const multiset<T> &vec)
{
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &vec)
{
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &pa)
{
  os << "(" << pa.first << "," << pa.second << ")";
  return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const map<TK, TV> &mp)
{
  os << "{";
  for (auto v : mp)
    os << v.first << "=>" << v.second << ",";
  os << "}";
  return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp)
{
  os << "{";
  for (auto v : mp)
    os << v.first << "=>" << v.second << ",";
  os << "}";
  return os;
}

template <typename T>
void reset(vector<T> &v, const T reset_to)
{
  for (auto &x : v)
    x = reset_to;
}
inline int popcount(const unsigned int x) { return __builtin_popcount(x); }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;

ll nC2(ll n)
{
  return n * (n - 1) / 2;
}

const int intinf = numeric_limits<int>::max();
const ll llinf = numeric_limits<ll>::max();
const pii udlr[4] = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};

//////////////////////////////   End Macros

// Modulo.h start----------------------------------------

#pragma once

#include <vector>
#include <iostream>
#include <cassert>

struct Modint;
std::vector<Modint> fact_mod;
std::vector<Modint> rev_fact_mod;

using namespace std;

// a x + b y = gcd(a, b)
int extgcd(const int a, const int b, int &x, int &y)
{
  // O(log max(a,b))
  int g = a;
  x = 1;
  y = 0;
  if (b != 0)
    g = extgcd(b, a % b, y, x), y -= (a / b) * x;
  return g;
}

int inv_mod(const int a, const int mod)
{
  int x, y;
  if (extgcd(a, mod, x, y) == 1)
    return (x + mod) % mod;
  else // unsolvable
    return 0;
}

struct Modint
{
  static int mod;
  long long value;
  Modint(long long value = 0LL) : value((value % mod + mod) % mod) {}
  inline bool operator==(const Modint &rhs) const { return value == rhs.value; }
  inline bool operator!=(const Modint &rhs) const { return !(*this == rhs); }
  inline Modint operator+() const { return *this; }
  inline Modint operator-() const { return Modint(-value); }
  inline Modint &operator+=(const Modint &rhs)
  {
    if ((value += rhs.value) >= mod)
      value -= mod;
    return *this;
  }
  inline Modint &operator-=(const Modint &rhs)
  {
    if ((value += mod - rhs.value) >= mod)
      value -= mod;
    return *this;
  }
  inline Modint &operator*=(const Modint &rhs)
  {
    (value *= rhs.value) %= mod;
    return *this;
  }
  Modint pow(long long k) const
  {
    assert(k >= 0);
    if (k == 0)
      return 1;
    Modint res = pow(k / 2);
    res *= res;
    if (k % 2 == 1)
      res *= *this;
    return res;
  }

  // for prime mod
  Modint inv() const { return pow(mod - 2); }
  inline Modint &operator/=(const Modint &rhs) { return *this *= rhs.inv(); }
};
int Modint::mod = 1000000007;
Modint operator+(const Modint &lhs, const Modint &rhs) { return Modint(lhs) += rhs; }
Modint operator-(const Modint &lhs, const Modint &rhs) { return Modint(lhs) -= rhs; }
Modint operator*(const Modint &lhs, const Modint &rhs) { return Modint(lhs) *= rhs; }
Modint operator/(const Modint &lhs, const Modint &rhs) { return Modint(lhs) /= rhs; }
ostream &operator>>(std::ostream &lhs, const Modint &rhs) { return lhs >> rhs.value; }
ostream &operator<<(std::ostream &lhs, const Modint &rhs) { return lhs << rhs.value; }

struct Combination
{
  std::vector<Modint> fact, ifact;
  Combination(int n = 0) : fact(n + 1), ifact(n + 1)
  {
    assert(n >= 0);
    fact[0] = 1;
    for (int i = 1; i <= n; i++)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; i--)
      ifact[i - 1] = ifact[i] * i;
  }
  Modint operator()(int n, int k)
  {
    assert(0 <= n and n <= fact.size());
    if (!(0 <= k and k <= n))
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};

// Modulo.h end----------------------------------------------

void solve()
{
  Modint::mod = 998244353;
  ll N, A, B;
  ll K;
  cin >> N >> A >> B >> K;

  vector<pll> xys;
  Modint ans = 0;
  Combination comb(N);
  forfl(x, 0, N)
  {
    if ((K - A * x) % B != 0)
      continue;

    ll y = (K - A * x) / B;
    if (0 <= y and y <= N)
      ans += comb(N, x) * comb(N, y);
  }
  cout << ans << endl;
}

int main()
{
  // cout << fixed << setprecision(15);
  solve();
  return 0;
}