Problem p03332 (C++)

Buggy submission (status: Runtime Error):
/*
URL https://
SCORE 0
AC false
WA false
TLE false
MLE false
TASK_TYPE
FAILURE_TYPE
NOTES
*/
#include <algorithm>
#include <cstdint>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std; // TODO Remove this

/* macros */
// loops
#define REP(i, n) for (i64 i = 0; i < static_cast<decltype(i)>(n); ++i)
#define REPR(i, n) for (i64 i = (n)-1; i >= static_cast<decltype(i)>(0); --i)
#define FOR(i, n, m) for (i64 i = (n); i < static_cast<decltype(i)>(m); ++i)
#define FORR(i, n, m) for (i64 i = (m)-1; i >= static_cast<decltype(i)>(n); --i)
#define EACH(x, xs) for (auto &x : (xs))
#define EACH_V(x, xs) for (auto x : (xs))

// helpers
#define CTR(x) (x).begin(), (x).end()

/* internal code */
namespace internal {
/* utils for std::tuple */
namespace tuple_utils {
template <size_t...> struct seq {};

template <size_t N, size_t... Is>
struct gen_seq : gen_seq<N - 1, N - 1, Is...> {};

template <size_t... Is> struct gen_seq<0, Is...> : seq<Is...> {};

template <class Tuple, size_t... Is>
void read(istream &stream, Tuple &t, seq<Is...>) {
  static_cast<void>((int[]){0, (void(stream >> get<Is>(t)), 0)...});
}

template <class Tuple, size_t... Is>
void print(ostream &stream, Tuple const &t, seq<Is...>) {
  static_cast<void>(
      (int[]){0, (void(stream << (Is == 0 ? "" : ", ") << get<Is>(t)), 0)...});
}

template <size_t I, class F, class A, class... Elems> struct ForEach {
  void operator()(A &arg, tuple<Elems...> const &t) const {
    F()(arg, get<I>(t));
    ForEach<I - 1, F, A, Elems...>()(arg, t);
  }

  void operator()(A &arg, tuple<Elems...> &t) const {
    F()(arg, get<I>(t));
    ForEach<I - 1, F, A, Elems...>()(arg, t);
  }
};

template <class F, class A, class... Elems> struct ForEach<0, F, A, Elems...> {
  void operator()(A &arg, tuple<Elems...> const &t) const {
    F()(arg, get<0>(t));
  }

  void operator()(A &arg, tuple<Elems...> &t) const { F()(arg, get<0>(t)); }
};

template <class F, class A, class... Elems>
void for_each(A &arg, tuple<Elems...> const &t) {
  ForEach<tuple_size<tuple<Elems...>>::value - 1, F, A, Elems...>()(arg, t);
}

template <class F, class A, class... Elems>
void for_each(A &arg, tuple<Elems...> &t) {
  ForEach<tuple_size<tuple<Elems...>>::value - 1, F, A, Elems...>()(arg, t);
}

struct hash_for_element {
  template <class V> void operator()(size_t &size, const V &v) const {
    size ^= hash<V>()(v);
  }
};
} // namespace tuple_utils

/* utils for std::vector */
namespace vector_utils {
template <typename V, int N> struct matrix_t {
  using type = std::vector<typename matrix_t<V, N - 1>::type>;
};
template <typename V> struct matrix_t<V, 0> {
  using type = V;
};

template <typename V, int N>
using Matrix = typename internal::vector_utils::matrix_t<V, N>::type;

template <typename V, typename It, int N> struct matrix_helper {
  static Matrix<V, N> create(const It &begin, const It &end,
                             const V &default_value) {
    return Matrix<V, N>(*begin, matrix_helper<V, It, N - 1>::create(
                                    begin + 1, end, default_value));
  }
};
template <typename V, typename It> struct matrix_helper<V, It, 0> {
  static Matrix<V, 0> create(const It &begin, const It &end,
                             const V &default_value) {
    return default_value;
  }
};
} // namespace vector_utils
} // namespace internal

/* Primitive types */
using i8 = int8_t;
using u8 = uint8_t;
using i16 = int16_t;
using u16 = uint16_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using usize = size_t;

/* Data structure type */
template <class T> using V = vector<T>; // TODO Replace with Vector
template <typename T> using Vector = internal::vector_utils::Matrix<T, 1>;
template <typename T, int N>
using Matrix = internal::vector_utils::Matrix<T, N>;
template <typename V> using OrderedSet = std::set<V>;
template <typename V> using HashSet = std::unordered_set<V>;
template <typename K, typename V> using OrderedMap = std::map<K, V>;
template <typename K, typename V> using HashMap = std::unordered_map<K, V>;

/* utils for std::vector */
template <typename V> std::vector<V> make_pre_allocated_vector(size_t N) {
  std::vector<V> retval;
  retval.reserve(N);
  return retval;
}

template <class V, int N>
Matrix<V, N> make_matrix(const std::array<size_t, N> &shape,
                         V default_value = V()) {
  return internal::vector_utils::matrix_helper<V, decltype(shape.begin()),
                                               N>::create(shape.begin(),
                                                          shape.end(),
                                                          default_value);
}
/* utils for STL containers */
template <class Iterator> struct Container {
  Container(const Iterator &begin, const Iterator &end)
      : m_begin(begin), m_end(end) {}
  const Iterator &begin() const { return this->m_begin; }
  const Iterator &end() const { return this->m_end; }
  Iterator m_begin;
  Iterator m_end;
};

/* utils for STL iterators */
template <typename Iterator, typename F> struct MappedIterator {
  MappedIterator(const Iterator &it, const F &function)
      : it(it), function(function) {}
  auto operator*() const { return this->function(this->it); }
  void operator++() { ++this->it; }
  void operator+=(size_t n) { this->it += n; }
  auto operator+(size_t n) const {
    return MappedIterator<Iterator, F>(this->it + n, this->function);
  }
  bool operator==(const MappedIterator<Iterator, F> &rhs) const {
    return this->it == rhs.it;
  }
  bool operator!=(const MappedIterator<Iterator, F> &rhs) const {
    return !(*this == rhs);
  }

private:
  Iterator it;
  F function;
};
template <typename Iterator, typename P> struct FilteredIterator {
  FilteredIterator(const Iterator &it, const Iterator &end, const P &predicate)
      : it(it), end(end), predicate(predicate) {
    if (this->it != end) {
      if (!predicate(this->it)) {
        this->increment();
      }
    }
  }
  decltype(auto) operator*() const { return *this->it; }
  auto operator->() const { return this->it; }
  void operator++() { this->increment(); }
  void operator+=(size_t n) {
    REP(i, n) { this->increment(); }
  }
  auto operator+(size_t n) const {
    auto retval = *this;
    retval += n;
    return retval;
  }
  bool operator==(const FilteredIterator<Iterator, P> &rhs) const {
    return this->it == rhs.it;
  }
  bool operator!=(const FilteredIterator<Iterator, P> &rhs) const {
    return !(*this == rhs);
  }

private:
  void increment() {
    if (this->it == this->end) {
      return;
    }
    ++this->it;
    while (this->it != this->end && !this->predicate(this->it)) {
      ++this->it;
    }
  }
  Iterator it;
  Iterator end;
  P predicate;
};
template <typename Iterator, typename ElementIterator>
struct FlattenedIterator {
  FlattenedIterator(const Iterator &it, const Iterator &end)
      : it(make_pair(it, ElementIterator())), end(end) {
    if (this->it.first != this->end) {
      this->it.second = it->begin();
    }
  }
  decltype(auto) operator*() const { return this->it; }
  const pair<Iterator, ElementIterator> *operator->() const {
    return &this->it;
  }
  void operator++() { this->increment(); }
  void operator+=(size_t n) {
    REP(i, n) { this->increment(); }
  }
  auto operator+(size_t n) const {
    auto retval = *this;
    retval += n;
    return retval;
  }
  bool
  operator==(const FlattenedIterator<Iterator, ElementIterator> &rhs) const {
    if (this->it.first != rhs.it.first) {
      return false;
    }
    if (this->it.first == this->end || rhs.it.first == rhs.end) {
      if (this->end == rhs.end) {
        return true;
      } else {
        return false;
      }
    } else {
      return this->it.second == rhs.it.second;
    }
  }
  bool
  operator!=(const FlattenedIterator<Iterator, ElementIterator> &rhs) const {
    return !(*this == rhs);
  }

private:
  void increment() {
    auto is_end = [this]() { return this->it.first == this->end; };
    auto is_valid = [this, &is_end]() {
      if (is_end())
        return false;
      if (this->it.second == this->it.first->end())
        return false;
      return true;
    };

    auto increment = [this]() {
      if (this->it.second == this->it.first->end()) {
        ++this->it.first;
        if (this->it.first != this->end) {
          this->it.second = this->it.first->begin();
        }
      } else {
        ++this->it.second;
      }
    };

    increment();
    while (!is_end() && !is_valid()) {
      increment();
    }
  }
  pair<Iterator, ElementIterator> it;
  Iterator end;
};

template <typename C, typename F> auto iterator_map(const C &c, F function) {
  using Iterator =
      std::remove_const_t<std::remove_reference_t<decltype(c.begin())>>;
  return Container<MappedIterator<Iterator, F>>(
      MappedIterator<Iterator, F>(c.begin(), function),
      MappedIterator<Iterator, F>(c.end(), function));
}

template <typename C, typename P>
auto iterator_filter(const C &c, P predicate) {
  using Iterator =
      std::remove_const_t<std::remove_reference_t<decltype(c.begin())>>;
  return Container<FilteredIterator<Iterator, P>>(
      FilteredIterator<Iterator, P>(c.begin(), c.end(), predicate),
      FilteredIterator<Iterator, P>(c.end(), c.end(), predicate));
}

template <typename C> auto iterator_flatten(const C &c) {
  using Iterator =
      std::remove_const_t<std::remove_reference_t<decltype(c.begin())>>;
  using ElementIterator = std::remove_const_t<
      std::remove_reference_t<decltype(c.begin()->begin())>>;
  return Container<FlattenedIterator<Iterator, ElementIterator>>(
      FlattenedIterator<Iterator, ElementIterator>(c.begin(), c.end()),
      FlattenedIterator<Iterator, ElementIterator>(c.end(), c.end()));
}

/* input */
template <class F, class S>
istream &operator>>(istream &stream, pair<F, S> &pair) {
  stream >> pair.first;
  stream >> pair.second;
  return stream;
}
template <class... Args>
istream &operator>>(istream &stream, tuple<Args...> &tuple) {
  internal::tuple_utils::read(
      stream, tuple, internal::tuple_utils::gen_seq<sizeof...(Args)>());
  return stream;
}

template <class T> T read() {
  T t;
  cin >> t;
  return t;
}
template <class F, class S> pair<F, S> read() {
  pair<F, S> p;
  cin >> p;
  return p;
}
template <class T1, class T2, class T3, class... Args>
tuple<T1, T2, T3, Args...> read() {
  tuple<T1, T2, T3, Args...> t;
  cin >> t;
  return t;
}
template <typename T, typename F = std::function<T()>>
Vector<T> read(const usize length, F r) {
  auto retval = make_pre_allocated_vector<T>(length);
  REP(i, length) { retval.emplace_back(r()); }
  return retval;
}

template <class T> Vector<T> read(const usize length) {
  return read<T>(length, [] { return read<T>(); });
}
template <class F, class S> Vector<pair<F, S>> read(const usize length) {
  return read<pair<F, S>>(length);
}
template <class T1, class T2, class T3, class... Args>
Vector<tuple<T1, T2, T3, Args...>> read(const usize length) {
  return read<tuple<T1, T2, T3, Args...>>(length);
}

/* debug output */
namespace debug {
template <typename T> struct oneline {
  std::string operator()(const T &t) const {
    std::ostringstream oss;
    oss << t;
    return oss.str();
  }
};
template <typename F, typename S> struct oneline<pair<F, S>> {
  std::string operator()(const pair<F, S> &p) const {
    std::ostringstream oss;
    oss << "{" << oneline<F>()(p.first) << ", " << oneline<S>()(p.second)
        << "}";
    return oss.str();
  }
};
struct oneline_tuple {
  template <class V>
  void operator()(vector<std::string> &strs, const V &v) const {
    strs.emplace_back(oneline<V>()(v));
  }
};
template <typename... Args> struct oneline<tuple<Args...>> {
  std::string operator()(const tuple<Args...> &t) const {
    std::ostringstream oss;
    std::vector<std::string> strs;
    internal::tuple_utils::for_each<oneline_tuple, std::vector<std::string>,
                                    Args...>(strs, t);
    oss << "{";
    REPR(i, strs.size()) {
      oss << strs[i];
      if (i != 0) {
        oss << ", ";
      }
    }
    oss << "}";
    return oss.str();
  }
};
template <> struct oneline<bool> {
  std::string operator()(const bool b) const { return b ? "true" : "false"; }
};
template <typename X> struct oneline<std::vector<X>> {
  std::string operator()(const Vector<X> &vec) const {
    std::string retval = "[";
    auto f = oneline<X>();
    REP(i, vec.size()) {
      retval += f(vec[i]);
      if (i != vec.size() - 1) {
        retval += ", ";
      }
    }
    retval += "]";
    return retval;
  }
};
template <typename X> struct oneline<OrderedSet<X>> {
  std::string operator()(const OrderedSet<X> &s) const {
    std::string retval = "{";
    auto f = oneline<X>();
    size_t ctr = 0;
    EACH(x, s) {
      retval += f(x);
      ctr += 1;
      if (ctr != s.size()) {
        retval += ", ";
      }
    }
    retval += "}";
    return retval;
  }
};
template <typename X> struct oneline<HashSet<X>> {
  std::string operator()(const HashSet<X> &s) const {
    std::string retval = "{";
    auto f = oneline<X>();
    size_t ctr = 0;
    EACH(x, s) {
      retval += f(x);
      ctr += 1;
      if (ctr != s.size()) {
        retval += ", ";
      }
    }
    retval += "}";
    return retval;
  }
};
template <typename K, typename V> struct oneline<OrderedMap<K, V>> {
  std::string operator()(const OrderedMap<K, V> &s) const {
    std::string retval = "{";
    auto f1 = oneline<K>();
    auto f2 = oneline<V>();
    size_t ctr = 0;
    EACH(x, s) {
      retval += f1(x.first);
      retval += ": ";
      retval += f2(x.second);
      ctr += 1;
      if (ctr != s.size()) {
        retval += ", ";
      }
    }
    retval += "}";
    return retval;
  }
};
template <typename K, typename V> struct oneline<HashMap<K, V>> {
  std::string operator()(const HashMap<K, V> &s) const {
    std::string retval = "{";
    auto f1 = oneline<K>();
    auto f2 = oneline<V>();
    size_t ctr = 0;
    EACH(x, s) {
      retval += f1(x.first);
      retval += ": ";
      retval += f2(x.second);
      ctr += 1;
      if (ctr != s.size()) {
        retval += ", ";
      }
    }
    retval += "}";
    return retval;
  }
};

template <typename V> struct keys { /* no implementation */
};
template <typename X> struct keys<std::vector<X>> {
  Vector<size_t> operator()(const Vector<X> &v) const {
    Vector<size_t> keys;
    REP(i, v.size()) { keys.emplace_back(i); }
    return keys;
  }
};
template <typename K, typename V> struct keys<OrderedMap<K, V>> {
  Vector<K> operator()(const OrderedMap<K, V> &c) const {
    Vector<K> keys;
    EACH(elem, c) { keys.emplace_back(elem.first); }
    return keys;
  }
};
template <typename K, typename V> struct keys<HashMap<K, V>> {
  Vector<K> operator()(const HashMap<K, V> &c) const {
    Vector<K> keys;
    EACH(elem, c) { keys.emplace_back(elem.first); }
    return keys;
  }
};
} // namespace debug

template <typename T> void dump(const T &t) {
  using namespace debug;
  std::cerr << oneline<T>()(t) << std::endl;
}
template <typename V1, typename V2, typename... Args>
void dump(const V1 &v1, const V2 &v2, const Args &...args) {
  using namespace debug;
  const auto x = std::make_tuple(v1, v2, args...);
  std::vector<std::string> strs;
  internal::tuple_utils::for_each<debug::oneline_tuple,
                                  std::vector<std::string>, Args...>(strs, x);
  REPR(i, strs.size()) {
    std::cerr << strs[i];
    if (i != 0) {
      std::cerr << ", ";
    }
  }
  std::cerr << std::endl;
}

template <typename C> std::string as_set(const C &ctr) {
  Vector<std::string> values;

  using namespace debug;
  EACH(x, ctr) { values.emplace_back(oneline<decltype(x)>()(x)); }
  std::string retval = "---\n";
  REP(i, values.size()) {
    retval += values[i];
    retval += "\n";
  }
  retval += "---";

  return retval;
}

template <typename C> std::string as_map(const C &ctr) {
  using namespace debug;

  auto ks = keys<C>()(ctr);
  Vector<std::string> keys;
  Vector<std::string> values;

  EACH(key, ks) {
    keys.emplace_back(oneline<decltype(key)>()(key));
    values.emplace_back(oneline<decltype(ctr.at(key))>()(ctr.at(key)));
  }
  size_t l = 0;
  EACH(key, keys) { l = std::max(l, key.size()); }
  std::string retval = "---\n";
  REP(i, values.size()) {
    retval += keys[i];
    REP(j, l - keys[i].size()) { retval += " "; }
    retval += ": ";
    retval += values[i];
    retval += "\n";
  }
  retval += "---";

  return retval;
}

template <typename C> std::string as_table(const C &ctr) {
  using namespace debug;
  auto rkeys = keys<C>()(ctr);
  auto ckeys = OrderedSet<std::string>();

  auto values =
      Vector<pair<std::string, OrderedMap<std::string, std::string>>>();

  /* Stringify all data */
  EACH(rkey, rkeys) {
    auto rkey_str = oneline<decltype(rkey)>()(rkey);
    values.emplace_back(rkey_str, OrderedMap<std::string, std::string>());

    auto row = ctr.at(rkey);
    auto ks = keys<decltype(row)>()(row);
    EACH(ckey, ks) {
      auto ckey_str = oneline<decltype(ckey)>()(ckey);
      ckeys.emplace(ckey_str);
      values.back().second.emplace(
          ckey_str, oneline<decltype(row.at(ckey))>()(row.at(ckey)));
    }
  }

  /* Calculate string length */
  size_t max_row_key_length = 0;
  EACH(value, values) {
    max_row_key_length = std::max(max_row_key_length, value.first.size());
  }

  OrderedMap<std::string, size_t> max_col_length;
  EACH(ckey, ckeys) { max_col_length.emplace(ckey, ckey.size()); }

  EACH(value, values) {
    EACH(elem, value.second) {
      auto ckey = elem.first;
      auto value = elem.second;
      max_col_length[ckey] = std::max(max_col_length[ckey], value.size());
    }
  }

  std::string retval = "---\n";
  /* Header */
  REP(i, max_row_key_length) { retval += " "; }
  retval += "  ";
  size_t cnt = 0;
  EACH(ckey, ckeys) {
    retval += ckey;
    REP(j, max_col_length[ckey] - ckey.size()) { retval += " "; }

    cnt += 1;
    if (cnt != ckeys.size()) {
      retval += ", ";
    }
  }
  retval += "\n------\n";

  /* Values */
  EACH(value, values) {
    retval += value.first;
    REP(i, max_row_key_length - value.first.size()) { retval += " "; }
    retval += "| ";

    size_t cnt = 0;
    EACH(ckey, ckeys) {
      auto v = std::string("");
      if (value.second.find(ckey) != value.second.end()) {
        v = value.second.at(ckey);
      }
      retval += v;
      REP(j, max_col_length[ckey] - v.size()) { retval += " "; }

      cnt += 1;
      if (cnt != ckeys.size()) {
        retval += ", ";
      }
    }

    retval += "\n";
  }
  retval += "---";
  return retval;
}

// Hash
namespace std {
template <class F, class S> struct hash<pair<F, S>> {
  size_t operator()(const pair<F, S> &p) const {
    return hash<F>()(p.first) ^ hash<S>()(p.second);
  }
};

template <class... Args> struct hash<tuple<Args...>> {
  size_t operator()(const tuple<Args...> &t) const {
    size_t retval = 0;

    internal::tuple_utils::for_each<internal::tuple_utils::hash_for_element,
                                    size_t, Args...>(retval, t);

    return retval;
  }
};
} // namespace std
#define MAIN
void body();

#ifndef MAIN
#include "common.cc"
#endif

/*
 * n^r
 */
template <class V> static V pow(V n, i64 r) {
  if (r == 0) {
    return 1;
  }

  auto r2 = r / 2;
  auto x2 = pow(n, r2);

  return x2 * x2 * ((r % 2 == 0) ? 1 : n);
}

static i64 gcd(i64 a, i64 b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

template <class Iterator>
static i64 gcd_ctr(const Iterator &begin, const Iterator &end) {
  if (begin == end) {
    return -1;
  } else {
    auto ans = *begin;
    auto it = begin;
    ++it;
    for (; it != end; ++it) {
      auto x = *it;
      ans = gcd(ans, x);
    }
    return ans;
  }
}

static i64 gcd_ctr(const V<i64> &xs) { return gcd_ctr(xs.begin(), xs.end()); }

static i64 lcm(i64 a, i64 b) {
  auto x = gcd(a, b);
  return a / x * b;
}

template <class Iterator>
static i64 lcm_ctr(const Iterator &begin, const Iterator &end) {
  if (begin == end) {
    return -1;
  } else {
    auto ans = *begin;
    auto it = begin;
    ++it;
    for (; it != end; ++it) {
      auto x = *it;
      ans = lcm(ans, x);
    }
    return ans;
  }
}

static i64 lcm_ctr(const V<i64> &xs) { return lcm_ctr(xs.begin(), xs.end()); }

template <class V> static V combination(V n, i64 r) {
  if (r == 0) {
    return 1;
  }

  V x = 1;
  FOR(d, 1, r + 1) {
    x *= n;
    n -= 1;
    x /= d;
  }
  return x;
}

static bool is_prime(i64 n) {
  if (n <= 1)
    return false;
  for (i64 i = 2; i * i <= n; i++) {
    if (n % i == 0)
      return false;
  }
  return true;
}

static V<i64> divisor(i64 n) {
  V<i64> res;
  for (i64 i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      res.push_back(i);
      if (i != n / i)
        res.push_back(n / i);
    }
  }
  return res;
}

static unordered_map<i64, size_t> prime_factor(i64 n) {
  unordered_map<i64, size_t> res;
  for (i64 i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      res[i] += 1;
      n /= i;
    }
  }
  if (n != 1)
    res[n] = 1;
  return res;
}

static pair<V<i64>, V<bool>> sieve(i64 n) {
  V<i64> prime;
  V<bool> is_prime_(n + 1, true);
  is_prime_[0] = is_prime_[1] = false;

  FOR(i, 2, n + 1) {
    if (is_prime_[i]) {
      prime.push_back(i);
      for (i64 j = 2 * i; j <= n; j += i) {
        is_prime_[j] = false;
      }
    }
  }
  return {prime, is_prime_};
}

#ifndef MAIN
#include "common.cc"
#include "math.cc"
#endif

namespace mod {
const i64 MOD = 998244353;

struct Integer {
  Integer() : value(0) {}
  Integer(i64 value) { update_value((value)); }

  Integer inverse() const { return pow(*this, MOD - 2); }

  Integer operator+(const Integer &rhs) const {
    return this->value + rhs.value;
  }
  Integer operator-(const Integer &rhs) const {
    return this->value - rhs.value;
  }

  Integer operator*(const Integer &rhs) const {
    return this->value * rhs.value;
  }

  Integer operator/(const Integer &rhs) const {
    return this->value * rhs.inverse().value;
  }

  void operator+=(const Integer &rhs) { update_value(this->value + rhs.value); }

  void operator-=(const Integer &rhs) { update_value(this->value - rhs.value); }

  void operator*=(const Integer &rhs) { update_value(this->value * rhs.value); }

  void operator/=(const Integer &rhs) {
    update_value(this->value * rhs.inverse().value);
  }

  bool operator==(const Integer &rhs) const { return this->value == rhs.value; }
  template <class V> bool operator==(V rhs) const { return this->value == rhs; }

  bool operator!=(const Integer &rhs) const { return this->value != rhs.value; }
  template <class V> bool operator!=(V rhs) const { return this->value != rhs; }

  const i64 &get() const { return this->value; }

private:
  void update_value(i64 new_value) {
    this->value = new_value;
    if (this->value < 0) {
      this->value += MOD;
    }
    if (this->value >= MOD) {
      this->value %= MOD;
    }
  }
  i64 value;
};

template <class V> static bool operator==(V lhs, const Integer &rhs) {
  return rhs == lhs;
}
template <class V> static bool operator!=(V lhs, const Integer &rhs) {
  return rhs != lhs;
}

struct fact {
  Integer value;
  Integer inverse;
};

static V<fact> fact_table(const size_t n) {
  V<fact> retval(n + 1);

  retval[0].value = 1;
  FOR(i, 1, n + 1) { retval[i].value = retval[i - 1].value * i; }

  retval[n].inverse = retval[n].value.inverse();
  REPR(i, n) { retval[i].inverse = retval[i + 1].inverse * (i + 1); }

  return retval;
}
} // namespace mod

namespace debug {
template <> struct oneline<mod::Integer> {
  std::string operator()(const mod::Integer &x) const {
    return oneline<decltype(x.get())>()(x.get()) + "(mod " +
           oneline<decltype(mod::MOD)>()(mod::MOD) + ")";
  }
};
} // namespace debug

// main function (DO NOT EDIT)
int main(int argc, char **argv) {
  cin.tie(0);
  ios_base::sync_with_stdio(false);

  cout << fixed;
  body();

  return 0;
}

void body() {
  auto N = read<i64>();
  auto A = read<i64>();
  auto B = read<i64>();
  auto K = read<u64>();

  auto fact = mod::fact_table(N);

  using namespace mod;
  Integer ans;

  REP(n, N + 1) {
    // A?n????
    auto R = K - n * A;
    if (R < 0)
      continue;
    if (R % B != 0)
      continue;

    i64 m = R / B;

    if (n > N || m > N)
      continue;

    /* A?????n??B?????m????? */
    auto a =
        fact[N].value * fact[N - n].value.inverse() * fact[n].value.inverse();
    auto b =
        fact[N].value * fact[N - m].value.inverse() * fact[m].value.inverse();
    ans += a * b;
  }
  cout << ans.get() << endl;
}


Fixed submission:
/*
URL https://
SCORE 0
AC false
WA false
TLE false
MLE false
TASK_TYPE
FAILURE_TYPE
NOTES
*/
#include <algorithm>
#include <cstdint>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std; // TODO Remove this

/* macros */
// loops
#define REP(i, n) for (i64 i = 0; i < static_cast<decltype(i)>(n); ++i)
#define REPR(i, n) for (i64 i = (n)-1; i >= static_cast<decltype(i)>(0); --i)
#define FOR(i, n, m) for (i64 i = (n); i < static_cast<decltype(i)>(m); ++i)
#define FORR(i, n, m) for (i64 i = (m)-1; i >= static_cast<decltype(i)>(n); --i)
#define EACH(x, xs) for (auto &x : (xs))
#define EACH_V(x, xs) for (auto x : (xs))

// helpers
#define CTR(x) (x).begin(), (x).end()

/* internal code */
namespace internal {
/* utils for std::tuple */
namespace tuple_utils {
template <size_t...> struct seq {};

template <size_t N, size_t... Is>
struct gen_seq : gen_seq<N - 1, N - 1, Is...> {};

template <size_t... Is> struct gen_seq<0, Is...> : seq<Is...> {};

template <class Tuple, size_t... Is>
void read(istream &stream, Tuple &t, seq<Is...>) {
  static_cast<void>((int[]){0, (void(stream >> get<Is>(t)), 0)...});
}

template <class Tuple, size_t... Is>
void print(ostream &stream, Tuple const &t, seq<Is...>) {
  static_cast<void>(
      (int[]){0, (void(stream << (Is == 0 ? "" : ", ") << get<Is>(t)), 0)...});
}

template <size_t I, class F, class A, class... Elems> struct ForEach {
  void operator()(A &arg, tuple<Elems...> const &t) const {
    F()(arg, get<I>(t));
    ForEach<I - 1, F, A, Elems...>()(arg, t);
  }

  void operator()(A &arg, tuple<Elems...> &t) const {
    F()(arg, get<I>(t));
    ForEach<I - 1, F, A, Elems...>()(arg, t);
  }
};

template <class F, class A, class... Elems> struct ForEach<0, F, A, Elems...> {
  void operator()(A &arg, tuple<Elems...> const &t) const {
    F()(arg, get<0>(t));
  }

  void operator()(A &arg, tuple<Elems...> &t) const { F()(arg, get<0>(t)); }
};

template <class F, class A, class... Elems>
void for_each(A &arg, tuple<Elems...> const &t) {
  ForEach<tuple_size<tuple<Elems...>>::value - 1, F, A, Elems...>()(arg, t);
}

template <class F, class A, class... Elems>
void for_each(A &arg, tuple<Elems...> &t) {
  ForEach<tuple_size<tuple<Elems...>>::value - 1, F, A, Elems...>()(arg, t);
}

struct hash_for_element {
  template <class V> void operator()(size_t &size, const V &v) const {
    size ^= hash<V>()(v);
  }
};
} // namespace tuple_utils

/* utils for std::vector */
namespace vector_utils {
template <typename V, int N> struct matrix_t {
  using type = std::vector<typename matrix_t<V, N - 1>::type>;
};
template <typename V> struct matrix_t<V, 0> {
  using type = V;
};

template <typename V, int N>
using Matrix = typename internal::vector_utils::matrix_t<V, N>::type;

template <typename V, typename It, int N> struct matrix_helper {
  static Matrix<V, N> create(const It &begin, const It &end,
                             const V &default_value) {
    return Matrix<V, N>(*begin, matrix_helper<V, It, N - 1>::create(
                                    begin + 1, end, default_value));
  }
};
template <typename V, typename It> struct matrix_helper<V, It, 0> {
  static Matrix<V, 0> create(const It &begin, const It &end,
                             const V &default_value) {
    return default_value;
  }
};
} // namespace vector_utils
} // namespace internal

/* Primitive types */
using i8 = int8_t;
using u8 = uint8_t;
using i16 = int16_t;
using u16 = uint16_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using usize = size_t;

/* Data structure type */
template <class T> using V = vector<T>; // TODO Replace with Vector
template <typename T> using Vector = internal::vector_utils::Matrix<T, 1>;
template <typename T, int N>
using Matrix = internal::vector_utils::Matrix<T, N>;
template <typename V> using OrderedSet = std::set<V>;
template <typename V> using HashSet = std::unordered_set<V>;
template <typename K, typename V> using OrderedMap = std::map<K, V>;
template <typename K, typename V> using HashMap = std::unordered_map<K, V>;

/* utils for std::vector */
template <typename V> std::vector<V> make_pre_allocated_vector(size_t N) {
  std::vector<V> retval;
  retval.reserve(N);
  return retval;
}

template <class V, int N>
Matrix<V, N> make_matrix(const std::array<size_t, N> &shape,
                         V default_value = V()) {
  return internal::vector_utils::matrix_helper<V, decltype(shape.begin()),
                                               N>::create(shape.begin(),
                                                          shape.end(),
                                                          default_value);
}
/* utils for STL containers */
template <class Iterator> struct Container {
  Container(const Iterator &begin, const Iterator &end)
      : m_begin(begin), m_end(end) {}
  const Iterator &begin() const { return this->m_begin; }
  const Iterator &end() const { return this->m_end; }
  Iterator m_begin;
  Iterator m_end;
};

/* utils for STL iterators */
template <typename Iterator, typename F> struct MappedIterator {
  MappedIterator(const Iterator &it, const F &function)
      : it(it), function(function) {}
  auto operator*() const { return this->function(this->it); }
  void operator++() { ++this->it; }
  void operator+=(size_t n) { this->it += n; }
  auto operator+(size_t n) const {
    return MappedIterator<Iterator, F>(this->it + n, this->function);
  }
  bool operator==(const MappedIterator<Iterator, F> &rhs) const {
    return this->it == rhs.it;
  }
  bool operator!=(const MappedIterator<Iterator, F> &rhs) const {
    return !(*this == rhs);
  }

private:
  Iterator it;
  F function;
};
template <typename Iterator, typename P> struct FilteredIterator {
  FilteredIterator(const Iterator &it, const Iterator &end, const P &predicate)
      : it(it), end(end), predicate(predicate) {
    if (this->it != end) {
      if (!predicate(this->it)) {
        this->increment();
      }
    }
  }
  decltype(auto) operator*() const { return *this->it; }
  auto operator->() const { return this->it; }
  void operator++() { this->increment(); }
  void operator+=(size_t n) {
    REP(i, n) { this->increment(); }
  }
  auto operator+(size_t n) const {
    auto retval = *this;
    retval += n;
    return retval;
  }
  bool operator==(const FilteredIterator<Iterator, P> &rhs) const {
    return this->it == rhs.it;
  }
  bool operator!=(const FilteredIterator<Iterator, P> &rhs) const {
    return !(*this == rhs);
  }

private:
  void increment() {
    if (this->it == this->end) {
      return;
    }
    ++this->it;
    while (this->it != this->end && !this->predicate(this->it)) {
      ++this->it;
    }
  }
  Iterator it;
  Iterator end;
  P predicate;
};
template <typename Iterator, typename ElementIterator>
struct FlattenedIterator {
  FlattenedIterator(const Iterator &it, const Iterator &end)
      : it(make_pair(it, ElementIterator())), end(end) {
    if (this->it.first != this->end) {
      this->it.second = it->begin();
    }
  }
  decltype(auto) operator*() const { return this->it; }
  const pair<Iterator, ElementIterator> *operator->() const {
    return &this->it;
  }
  void operator++() { this->increment(); }
  void operator+=(size_t n) {
    REP(i, n) { this->increment(); }
  }
  auto operator+(size_t n) const {
    auto retval = *this;
    retval += n;
    return retval;
  }
  bool
  operator==(const FlattenedIterator<Iterator, ElementIterator> &rhs) const {
    if (this->it.first != rhs.it.first) {
      return false;
    }
    if (this->it.first == this->end || rhs.it.first == rhs.end) {
      if (this->end == rhs.end) {
        return true;
      } else {
        return false;
      }
    } else {
      return this->it.second == rhs.it.second;
    }
  }
  bool
  operator!=(const FlattenedIterator<Iterator, ElementIterator> &rhs) const {
    return !(*this == rhs);
  }

private:
  void increment() {
    auto is_end = [this]() { return this->it.first == this->end; };
    auto is_valid = [this, &is_end]() {
      if (is_end())
        return false;
      if (this->it.second == this->it.first->end())
        return false;
      return true;
    };

    auto increment = [this]() {
      if (this->it.second == this->it.first->end()) {
        ++this->it.first;
        if (this->it.first != this->end) {
          this->it.second = this->it.first->begin();
        }
      } else {
        ++this->it.second;
      }
    };

    increment();
    while (!is_end() && !is_valid()) {
      increment();
    }
  }
  pair<Iterator, ElementIterator> it;
  Iterator end;
};

template <typename C, typename F> auto iterator_map(const C &c, F function) {
  using Iterator =
      std::remove_const_t<std::remove_reference_t<decltype(c.begin())>>;
  return Container<MappedIterator<Iterator, F>>(
      MappedIterator<Iterator, F>(c.begin(), function),
      MappedIterator<Iterator, F>(c.end(), function));
}

template <typename C, typename P>
auto iterator_filter(const C &c, P predicate) {
  using Iterator =
      std::remove_const_t<std::remove_reference_t<decltype(c.begin())>>;
  return Container<FilteredIterator<Iterator, P>>(
      FilteredIterator<Iterator, P>(c.begin(), c.end(), predicate),
      FilteredIterator<Iterator, P>(c.end(), c.end(), predicate));
}

template <typename C> auto iterator_flatten(const C &c) {
  using Iterator =
      std::remove_const_t<std::remove_reference_t<decltype(c.begin())>>;
  using ElementIterator = std::remove_const_t<
      std::remove_reference_t<decltype(c.begin()->begin())>>;
  return Container<FlattenedIterator<Iterator, ElementIterator>>(
      FlattenedIterator<Iterator, ElementIterator>(c.begin(), c.end()),
      FlattenedIterator<Iterator, ElementIterator>(c.end(), c.end()));
}

/* input */
template <class F, class S>
istream &operator>>(istream &stream, pair<F, S> &pair) {
  stream >> pair.first;
  stream >> pair.second;
  return stream;
}
template <class... Args>
istream &operator>>(istream &stream, tuple<Args...> &tuple) {
  internal::tuple_utils::read(
      stream, tuple, internal::tuple_utils::gen_seq<sizeof...(Args)>());
  return stream;
}

template <class T> T read() {
  T t;
  cin >> t;
  return t;
}
template <class F, class S> pair<F, S> read() {
  pair<F, S> p;
  cin >> p;
  return p;
}
template <class T1, class T2, class T3, class... Args>
tuple<T1, T2, T3, Args...> read() {
  tuple<T1, T2, T3, Args...> t;
  cin >> t;
  return t;
}
template <typename T, typename F = std::function<T()>>
Vector<T> read(const usize length, F r) {
  auto retval = make_pre_allocated_vector<T>(length);
  REP(i, length) { retval.emplace_back(r()); }
  return retval;
}

template <class T> Vector<T> read(const usize length) {
  return read<T>(length, [] { return read<T>(); });
}
template <class F, class S> Vector<pair<F, S>> read(const usize length) {
  return read<pair<F, S>>(length);
}
template <class T1, class T2, class T3, class... Args>
Vector<tuple<T1, T2, T3, Args...>> read(const usize length) {
  return read<tuple<T1, T2, T3, Args...>>(length);
}

/* debug output */
namespace debug {
template <typename T> struct oneline {
  std::string operator()(const T &t) const {
    std::ostringstream oss;
    oss << t;
    return oss.str();
  }
};
template <typename F, typename S> struct oneline<pair<F, S>> {
  std::string operator()(const pair<F, S> &p) const {
    std::ostringstream oss;
    oss << "{" << oneline<F>()(p.first) << ", " << oneline<S>()(p.second)
        << "}";
    return oss.str();
  }
};
struct oneline_tuple {
  template <class V>
  void operator()(vector<std::string> &strs, const V &v) const {
    strs.emplace_back(oneline<V>()(v));
  }
};
template <typename... Args> struct oneline<tuple<Args...>> {
  std::string operator()(const tuple<Args...> &t) const {
    std::ostringstream oss;
    std::vector<std::string> strs;
    internal::tuple_utils::for_each<oneline_tuple, std::vector<std::string>,
                                    Args...>(strs, t);
    oss << "{";
    REPR(i, strs.size()) {
      oss << strs[i];
      if (i != 0) {
        oss << ", ";
      }
    }
    oss << "}";
    return oss.str();
  }
};
template <> struct oneline<bool> {
  std::string operator()(const bool b) const { return b ? "true" : "false"; }
};
template <typename X> struct oneline<std::vector<X>> {
  std::string operator()(const Vector<X> &vec) const {
    std::string retval = "[";
    auto f = oneline<X>();
    REP(i, vec.size()) {
      retval += f(vec[i]);
      if (i != vec.size() - 1) {
        retval += ", ";
      }
    }
    retval += "]";
    return retval;
  }
};
template <typename X> struct oneline<OrderedSet<X>> {
  std::string operator()(const OrderedSet<X> &s) const {
    std::string retval = "{";
    auto f = oneline<X>();
    size_t ctr = 0;
    EACH(x, s) {
      retval += f(x);
      ctr += 1;
      if (ctr != s.size()) {
        retval += ", ";
      }
    }
    retval += "}";
    return retval;
  }
};
template <typename X> struct oneline<HashSet<X>> {
  std::string operator()(const HashSet<X> &s) const {
    std::string retval = "{";
    auto f = oneline<X>();
    size_t ctr = 0;
    EACH(x, s) {
      retval += f(x);
      ctr += 1;
      if (ctr != s.size()) {
        retval += ", ";
      }
    }
    retval += "}";
    return retval;
  }
};
template <typename K, typename V> struct oneline<OrderedMap<K, V>> {
  std::string operator()(const OrderedMap<K, V> &s) const {
    std::string retval = "{";
    auto f1 = oneline<K>();
    auto f2 = oneline<V>();
    size_t ctr = 0;
    EACH(x, s) {
      retval += f1(x.first);
      retval += ": ";
      retval += f2(x.second);
      ctr += 1;
      if (ctr != s.size()) {
        retval += ", ";
      }
    }
    retval += "}";
    return retval;
  }
};
template <typename K, typename V> struct oneline<HashMap<K, V>> {
  std::string operator()(const HashMap<K, V> &s) const {
    std::string retval = "{";
    auto f1 = oneline<K>();
    auto f2 = oneline<V>();
    size_t ctr = 0;
    EACH(x, s) {
      retval += f1(x.first);
      retval += ": ";
      retval += f2(x.second);
      ctr += 1;
      if (ctr != s.size()) {
        retval += ", ";
      }
    }
    retval += "}";
    return retval;
  }
};

template <typename V> struct keys { /* no implementation */
};
template <typename X> struct keys<std::vector<X>> {
  Vector<size_t> operator()(const Vector<X> &v) const {
    Vector<size_t> keys;
    REP(i, v.size()) { keys.emplace_back(i); }
    return keys;
  }
};
template <typename K, typename V> struct keys<OrderedMap<K, V>> {
  Vector<K> operator()(const OrderedMap<K, V> &c) const {
    Vector<K> keys;
    EACH(elem, c) { keys.emplace_back(elem.first); }
    return keys;
  }
};
template <typename K, typename V> struct keys<HashMap<K, V>> {
  Vector<K> operator()(const HashMap<K, V> &c) const {
    Vector<K> keys;
    EACH(elem, c) { keys.emplace_back(elem.first); }
    return keys;
  }
};
} // namespace debug

template <typename T> void dump(const T &t) {
  using namespace debug;
  std::cerr << oneline<T>()(t) << std::endl;
}
template <typename V1, typename V2, typename... Args>
void dump(const V1 &v1, const V2 &v2, const Args &...args) {
  using namespace debug;
  const auto x = std::make_tuple(v1, v2, args...);
  std::vector<std::string> strs;
  internal::tuple_utils::for_each<debug::oneline_tuple,
                                  std::vector<std::string>, Args...>(strs, x);
  REPR(i, strs.size()) {
    std::cerr << strs[i];
    if (i != 0) {
      std::cerr << ", ";
    }
  }
  std::cerr << std::endl;
}

template <typename C> std::string as_set(const C &ctr) {
  Vector<std::string> values;

  using namespace debug;
  EACH(x, ctr) { values.emplace_back(oneline<decltype(x)>()(x)); }
  std::string retval = "---\n";
  REP(i, values.size()) {
    retval += values[i];
    retval += "\n";
  }
  retval += "---";

  return retval;
}

template <typename C> std::string as_map(const C &ctr) {
  using namespace debug;

  auto ks = keys<C>()(ctr);
  Vector<std::string> keys;
  Vector<std::string> values;

  EACH(key, ks) {
    keys.emplace_back(oneline<decltype(key)>()(key));
    values.emplace_back(oneline<decltype(ctr.at(key))>()(ctr.at(key)));
  }
  size_t l = 0;
  EACH(key, keys) { l = std::max(l, key.size()); }
  std::string retval = "---\n";
  REP(i, values.size()) {
    retval += keys[i];
    REP(j, l - keys[i].size()) { retval += " "; }
    retval += ": ";
    retval += values[i];
    retval += "\n";
  }
  retval += "---";

  return retval;
}

template <typename C> std::string as_table(const C &ctr) {
  using namespace debug;
  auto rkeys = keys<C>()(ctr);
  auto ckeys = OrderedSet<std::string>();

  auto values =
      Vector<pair<std::string, OrderedMap<std::string, std::string>>>();

  /* Stringify all data */
  EACH(rkey, rkeys) {
    auto rkey_str = oneline<decltype(rkey)>()(rkey);
    values.emplace_back(rkey_str, OrderedMap<std::string, std::string>());

    auto row = ctr.at(rkey);
    auto ks = keys<decltype(row)>()(row);
    EACH(ckey, ks) {
      auto ckey_str = oneline<decltype(ckey)>()(ckey);
      ckeys.emplace(ckey_str);
      values.back().second.emplace(
          ckey_str, oneline<decltype(row.at(ckey))>()(row.at(ckey)));
    }
  }

  /* Calculate string length */
  size_t max_row_key_length = 0;
  EACH(value, values) {
    max_row_key_length = std::max(max_row_key_length, value.first.size());
  }

  OrderedMap<std::string, size_t> max_col_length;
  EACH(ckey, ckeys) { max_col_length.emplace(ckey, ckey.size()); }

  EACH(value, values) {
    EACH(elem, value.second) {
      auto ckey = elem.first;
      auto value = elem.second;
      max_col_length[ckey] = std::max(max_col_length[ckey], value.size());
    }
  }

  std::string retval = "---\n";
  /* Header */
  REP(i, max_row_key_length) { retval += " "; }
  retval += "  ";
  size_t cnt = 0;
  EACH(ckey, ckeys) {
    retval += ckey;
    REP(j, max_col_length[ckey] - ckey.size()) { retval += " "; }

    cnt += 1;
    if (cnt != ckeys.size()) {
      retval += ", ";
    }
  }
  retval += "\n------\n";

  /* Values */
  EACH(value, values) {
    retval += value.first;
    REP(i, max_row_key_length - value.first.size()) { retval += " "; }
    retval += "| ";

    size_t cnt = 0;
    EACH(ckey, ckeys) {
      auto v = std::string("");
      if (value.second.find(ckey) != value.second.end()) {
        v = value.second.at(ckey);
      }
      retval += v;
      REP(j, max_col_length[ckey] - v.size()) { retval += " "; }

      cnt += 1;
      if (cnt != ckeys.size()) {
        retval += ", ";
      }
    }

    retval += "\n";
  }
  retval += "---";
  return retval;
}

// Hash
namespace std {
template <class F, class S> struct hash<pair<F, S>> {
  size_t operator()(const pair<F, S> &p) const {
    return hash<F>()(p.first) ^ hash<S>()(p.second);
  }
};

template <class... Args> struct hash<tuple<Args...>> {
  size_t operator()(const tuple<Args...> &t) const {
    size_t retval = 0;

    internal::tuple_utils::for_each<internal::tuple_utils::hash_for_element,
                                    size_t, Args...>(retval, t);

    return retval;
  }
};
} // namespace std
#define MAIN
void body();

#ifndef MAIN
#include "common.cc"
#endif

/*
 * n^r
 */
template <class V> static V pow(V n, i64 r) {
  if (r == 0) {
    return 1;
  }

  auto r2 = r / 2;
  auto x2 = pow(n, r2);

  return x2 * x2 * ((r % 2 == 0) ? 1 : n);
}

static i64 gcd(i64 a, i64 b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

template <class Iterator>
static i64 gcd_ctr(const Iterator &begin, const Iterator &end) {
  if (begin == end) {
    return -1;
  } else {
    auto ans = *begin;
    auto it = begin;
    ++it;
    for (; it != end; ++it) {
      auto x = *it;
      ans = gcd(ans, x);
    }
    return ans;
  }
}

static i64 gcd_ctr(const V<i64> &xs) { return gcd_ctr(xs.begin(), xs.end()); }

static i64 lcm(i64 a, i64 b) {
  auto x = gcd(a, b);
  return a / x * b;
}

template <class Iterator>
static i64 lcm_ctr(const Iterator &begin, const Iterator &end) {
  if (begin == end) {
    return -1;
  } else {
    auto ans = *begin;
    auto it = begin;
    ++it;
    for (; it != end; ++it) {
      auto x = *it;
      ans = lcm(ans, x);
    }
    return ans;
  }
}

static i64 lcm_ctr(const V<i64> &xs) { return lcm_ctr(xs.begin(), xs.end()); }

template <class V> static V combination(V n, i64 r) {
  if (r == 0) {
    return 1;
  }

  V x = 1;
  FOR(d, 1, r + 1) {
    x *= n;
    n -= 1;
    x /= d;
  }
  return x;
}

static bool is_prime(i64 n) {
  if (n <= 1)
    return false;
  for (i64 i = 2; i * i <= n; i++) {
    if (n % i == 0)
      return false;
  }
  return true;
}

static V<i64> divisor(i64 n) {
  V<i64> res;
  for (i64 i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      res.push_back(i);
      if (i != n / i)
        res.push_back(n / i);
    }
  }
  return res;
}

static unordered_map<i64, size_t> prime_factor(i64 n) {
  unordered_map<i64, size_t> res;
  for (i64 i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      res[i] += 1;
      n /= i;
    }
  }
  if (n != 1)
    res[n] = 1;
  return res;
}

static pair<V<i64>, V<bool>> sieve(i64 n) {
  V<i64> prime;
  V<bool> is_prime_(n + 1, true);
  is_prime_[0] = is_prime_[1] = false;

  FOR(i, 2, n + 1) {
    if (is_prime_[i]) {
      prime.push_back(i);
      for (i64 j = 2 * i; j <= n; j += i) {
        is_prime_[j] = false;
      }
    }
  }
  return {prime, is_prime_};
}

#ifndef MAIN
#include "common.cc"
#include "math.cc"
#endif

namespace mod {
const i64 MOD = 998244353;

struct Integer {
  Integer() : value(0) {}
  Integer(i64 value) { update_value((value)); }

  Integer inverse() const { return pow(*this, MOD - 2); }

  Integer operator+(const Integer &rhs) const {
    return this->value + rhs.value;
  }
  Integer operator-(const Integer &rhs) const {
    return this->value - rhs.value;
  }

  Integer operator*(const Integer &rhs) const {
    return this->value * rhs.value;
  }

  Integer operator/(const Integer &rhs) const {
    return this->value * rhs.inverse().value;
  }

  void operator+=(const Integer &rhs) { update_value(this->value + rhs.value); }

  void operator-=(const Integer &rhs) { update_value(this->value - rhs.value); }

  void operator*=(const Integer &rhs) { update_value(this->value * rhs.value); }

  void operator/=(const Integer &rhs) {
    update_value(this->value * rhs.inverse().value);
  }

  bool operator==(const Integer &rhs) const { return this->value == rhs.value; }
  template <class V> bool operator==(V rhs) const { return this->value == rhs; }

  bool operator!=(const Integer &rhs) const { return this->value != rhs.value; }
  template <class V> bool operator!=(V rhs) const { return this->value != rhs; }

  const i64 &get() const { return this->value; }

private:
  void update_value(i64 new_value) {
    this->value = new_value;
    if (this->value < 0) {
      this->value += MOD;
    }
    if (this->value >= MOD) {
      this->value %= MOD;
    }
  }
  i64 value;
};

template <class V> static bool operator==(V lhs, const Integer &rhs) {
  return rhs == lhs;
}
template <class V> static bool operator!=(V lhs, const Integer &rhs) {
  return rhs != lhs;
}

struct fact {
  Integer value;
  Integer inverse;
};

static V<fact> fact_table(const size_t n) {
  V<fact> retval(n + 1);

  retval[0].value = 1;
  FOR(i, 1, n + 1) { retval[i].value = retval[i - 1].value * i; }

  retval[n].inverse = retval[n].value.inverse();
  REPR(i, n) { retval[i].inverse = retval[i + 1].inverse * (i + 1); }

  return retval;
}
} // namespace mod

namespace debug {
template <> struct oneline<mod::Integer> {
  std::string operator()(const mod::Integer &x) const {
    return oneline<decltype(x.get())>()(x.get()) + "(mod " +
           oneline<decltype(mod::MOD)>()(mod::MOD) + ")";
  }
};
} // namespace debug

// main function (DO NOT EDIT)
int main(int argc, char **argv) {
  cin.tie(0);
  ios_base::sync_with_stdio(false);

  cout << fixed;
  body();

  return 0;
}

void body() {
  auto N = read<i64>();
  auto A = read<i64>();
  auto B = read<i64>();
  auto K = read<i64>();

  auto fact = mod::fact_table(N);

  using namespace mod;
  Integer ans;

  REP(n, N + 1) {
    // A?n????
    auto R = K - n * A;
    if (R < 0)
      continue;
    if (R % B != 0)
      continue;

    i64 m = R / B;

    if (n > N || m > N)
      continue;

    /* A?????n??B?????m????? */
    auto a =
        fact[N].value * fact[N - n].value.inverse() * fact[n].value.inverse();
    auto b =
        fact[N].value * fact[N - m].value.inverse() * fact[m].value.inverse();
    ans += a * b;
  }
  cout << ans.get() << endl;
}