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

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);
            }
        };
    }

    /* 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;
            }
        };
    }
}


/* 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;
        }
    };
}

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;
        }
    };
}
#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 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) + ")";
        }
    };
}


// 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;
}


Measured memory_bytes: 4992