#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

#include <limits>
#include <type_traits>

namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
    if constexpr (cond_v) {
        return std::forward<Then>(then);
    } else {
        return std::forward<OrElse>(or_else);
    }
}

// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;

template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;

// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;

// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long int> { using type = __uint128_t; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;

} // namespace suisen

// ! type aliases
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T, typename U>
using umap = std::unordered_map<T, U>;

// ! macros (capital: internal macro)
#define OVERLOAD2(_1,_2,name,...) name
#define OVERLOAD3(_1,_2,_3,name,...) name
#define OVERLOAD4(_1,_2,_3,_4,name,...) name

#define REP4(i,l,r,s)  for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define REP3(i,l,r)    REP4(i,l,r,1)
#define REP2(i,n)      REP3(i,0,n)
#define REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define REPINF2(i,l)   REPINF3(i,l,1)
#define REPINF1(i)     REPINF2(i,0)
#define RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))
#define RREP3(i,l,r)   RREP4(i,l,r,1)
#define RREP2(i,n)     RREP3(i,0,n)

#define rep(...)    OVERLOAD4(__VA_ARGS__, REP4   , REP3   , REP2   )(__VA_ARGS__)
#define rrep(...)   OVERLOAD4(__VA_ARGS__, RREP4  , RREP3  , RREP2  )(__VA_ARGS__)
#define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__)

#define CAT_I(a, b) a##b
#define CAT(a, b) CAT_I(a, b)
#define UNIQVAR(tag) CAT(tag, __LINE__)
#define loop(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;)

#define all(iterable) std::begin(iterable), std::end(iterable)
#define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__)

#ifdef LOCAL
#  define debug(...) debug_internal(#__VA_ARGS__, __VA_ARGS__)

template <class T, class... Args>
void debug_internal(const char* s, T&& first, Args&&... args) {
    constexpr const char* prefix = "[\033[32mDEBUG\033[m] ";
    constexpr const char* open_brakets = sizeof...(args) == 0 ? "" : "(";
    constexpr const char* close_brakets = sizeof...(args) == 0 ? "" : ")";
    std::cerr << prefix << open_brakets << s << close_brakets << ": " << open_brakets << std::forward<T>(first);
    ((std::cerr << ", " << std::forward<Args>(args)), ...);
    std::cerr << close_brakets << "\n";
}

#else
#  define debug(...) void(0)
#endif

// ! I/O utilities

// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U> &a) {
    return out << a.first << ' ' << a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::ostream& operator<<(std::ostream& out, const std::tuple<Args...> &a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
        return out;
    } else {
        out << std::get<N>(a);
        if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) {
            out << ' ';
        }
        return operator<<<N + 1>(out, a);
    }
}
// vector
template <typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T> &a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
// array
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& out, const std::array<T, N> &a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head &head, const Tail &...tails) {
    std::cout << head;
    if (sizeof...(tails)) std::cout << ' ';
    print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
    for (auto it = v.begin(); it != v.end();) {
        std::cout << *it;
        if (++it != v.end()) std::cout << sep;
    }
    std::cout << end;
}

// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U> &a) {
    return in >> a.first >> a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::istream& operator>>(std::istream& in, std::tuple<Args...> &a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
        return in;
    } else {
        return operator>><N + 1>(in >> std::get<N>(a), a);
    }
}
// vector
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T> &a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
// array
template <typename T, size_t N>
std::istream& operator>>(std::istream& in, std::array<T, N> &a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
template <typename ...Args>
void read(Args &...args) {
    ( std::cin >> ... >> args );
}

// ! integral utilities

// Returns pow(-1, n)
template <typename T>
constexpr inline int pow_m1(T n) {
    return -(n & 1) | 1;
}
// Returns pow(-1, n)
template <>
constexpr inline int pow_m1<bool>(bool n) {
    return -int(n) | 1;
}

// Returns floor(x / y)
template <typename T>
constexpr inline T fld(const T x, const T y) {
    return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
}
template <typename T>
constexpr inline T cld(const T x, const T y) {
    return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
}

template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcount(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcount(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcountll(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }
template <typename T>
constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }
template <typename T>
constexpr inline int ceil_log2(const T x)  { return floor_log2(x) + ((x & -x) != x); }
template <typename T>
constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }
template <typename T>
constexpr inline int parity(const T x) { return popcount(x) & 1; }

struct all_subset {
    struct all_subset_iter {
        const int s; int t;
        constexpr all_subset_iter(int s) : s(s), t(s + 1) {}
        constexpr auto operator*() const { return t; }
        constexpr auto operator++() {}
        constexpr auto operator!=(std::nullptr_t) { return t ? (--t &= s, true) : false; }
    };
    int s;
    constexpr all_subset(int s) : s(s) {}
    constexpr auto begin() { return all_subset_iter(s); }
    constexpr auto end()   { return nullptr; }
};

// ! container

template <typename T, typename Comparator, suisen::constraints_t<suisen::is_comparator<Comparator, T>> = nullptr>
auto priqueue_comp(const Comparator comparator) {
    return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}

template <typename Iterable>
auto isize(const Iterable &iterable) -> decltype(int(iterable.size())) {
    return iterable.size();
}

template <typename T, typename Gen, suisen::constraints_t<suisen::is_same_as_invoke_result<T, Gen, int>> = nullptr>
auto generate_vector(int n, Gen generator) {
    std::vector<T> v(n);
    for (int i = 0; i < n; ++i) v[i] = generator(i);
    return v;
}
template <typename T>
auto generate_range_vector(T l, T r) {
    return generate_vector(r - l, [l](int i) { return l + i; });
}
template <typename T>
auto generate_range_vector(T n) {
    return generate_range_vector(0, n);
}

template <typename T>
void sort_unique_erase(std::vector<T> &a) {
    std::sort(a.begin(), a.end());
    a.erase(std::unique(a.begin(), a.end()), a.end());
}

template <typename InputIterator, typename BiConsumer>
auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {
    if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);
}
template <typename Container, typename BiConsumer>
auto foreach_adjacent_values(Container c, BiConsumer f) -> decltype(c.begin(), c.end(), void()){
    foreach_adjacent_values(c.begin(), c.end(), f);
}

// ! other utilities

// x <- min(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmin(T &x, const T &y) {
    if (y >= x) return false;
    x = y;
    return true;
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T &x, const T &y) {
    if (y <= x) return false;
    x = y;
    return true;
}

namespace suisen {}
using namespace suisen;
using namespace std;

struct io_setup {
    io_setup(int precision = 20) {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(precision);
    }
} io_setup_ {};

// ! code from here

#include <atcoder/modint>
#include <atcoder/convolution>

using mint = atcoder::modint998244353;

std::istream& operator>>(std::istream& in, mint &a) {
    long long e; in >> e; a = e;
    return in;
}

std::ostream& operator<<(std::ostream& out, const mint &a) {
    out << a.val();
    return out;
}

#include <deque>
#include <vector>

#include <algorithm>
#include <cassert>
#include <iostream>

namespace suisen {
template <typename mint>
class inv_mods {
    public:
        inv_mods() {}
        inv_mods(int n) { ensure(n); }
        const mint& operator[](int i) const {
            ensure(i);
            return invs[i];
        }
        static void ensure(int n) {
            int sz = invs.size();
            if (sz < 2) invs = {0, 1}, sz = 2;
            if (sz < n + 1) {
                invs.resize(n + 1);
                for (int i = sz; i <= n; ++i) invs[i] = mint(mod - mod / i) * invs[mod % i];
            }
        }
    private:
        static std::vector<mint> invs;
        static constexpr int mod = mint::mod();
};
template <typename mint>
std::vector<mint> inv_mods<mint>::invs{};
}

namespace suisen {

template <typename mint>
using convolution_t = std::vector<mint> (*)(const std::vector<mint> &, const std::vector<mint> &);

template <typename mint>
class FPS : public std::vector<mint> {
    public:
        using std::vector<mint>::vector;

        FPS(const std::initializer_list<mint> l) : std::vector<mint>::vector(l) {}
        FPS(const std::vector<mint> &v) : std::vector<mint>::vector(v) {}
        FPS(std::vector<mint> &&v) : std::vector<mint>::vector(std::move(v)) {}

        static void set_multiplication(convolution_t<mint> multiplication) {
            FPS<mint>::mult = multiplication;
        }

        inline const mint  operator[](int n) const noexcept { return n <= deg() ? unsafe_get(n) : 0; }
        inline       mint& operator[](int n)       noexcept { ensure_deg(n); return unsafe_get(n); }

        inline int size() const noexcept { return std::vector<mint>::size(); }
        inline int deg()  const noexcept { return size() - 1; }
        inline int normalize() {
            while (this->size() and this->back() == 0) this->pop_back();
            return deg();
        }
        inline FPS& pre_inplace(int max_deg) noexcept {
            if (deg() > max_deg) this->resize(std::max(0, max_deg + 1));
            return *this;
        }
        inline FPS pre(int max_deg) const noexcept { return FPS(*this).pre_inplace(max_deg); }

        inline FPS operator+() const { return FPS(*this); }
        FPS operator-() const {
            FPS f(*this);
            for (auto &e : f) e = mint::mod() - e;
            return f;
        }
        inline FPS& operator++() { ++(*this)[0]; return *this; }
        inline FPS& operator--() { --(*this)[0]; return *this; }
        inline FPS& operator+=(const mint x) { (*this)[0] += x; return *this; }
        inline FPS& operator-=(const mint x) { (*this)[0] -= x; return *this; }
        FPS& operator+=(const FPS &g) {
            ensure_deg(g.deg());
            for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) += g.unsafe_get(i);
            return *this;
        }
        FPS& operator-=(const FPS &g) {
            ensure_deg(g.deg());
            for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) -= g.unsafe_get(i);
            return *this;
        }
        inline FPS& operator*=(const FPS  &g) { return *this = FPS<mint>::mult(*this, g); }
        inline FPS& operator*=(      FPS &&g) { return *this = FPS<mint>::mult(*this, g); }
        inline FPS& operator*=(const mint x) {
            for (auto &e : *this) e *= x;
            return *this;
        }
        FPS& operator/=(FPS &&g) {
            const int fd = normalize(), gd = g.normalize();
            assert(gd >= 0);
            if (fd < gd) { this->clear(); return *this; }
            if (gd == 0) return *this *= g.unsafe_get(0).inv();
            static constexpr int THRESHOLD_NAIVE_POLY_QUOTIENT = 256;
            if (gd <= THRESHOLD_NAIVE_POLY_QUOTIENT) {
                *this = std::move(naive_div_inplace(std::move(g), gd).first);
                return *this;
            }
            std::reverse(this->begin(), this->end()), std::reverse(g.begin(), g.end());
            const int k = fd - gd;
            *this *= g.inv_inplace(k), this->resize(k + 1);
            std::reverse(this->begin(), this->end());
            return *this;
        }
        FPS& operator%=(FPS &&g) {
            int fd = normalize(), gd = g.normalize();
            assert(gd >= 0);
            if (fd < gd) return *this;
            if (gd == 0) { this->clear(); return *this; }
            static constexpr int THRESHOLD_NAIVE_REMAINDER = 256;
            if (gd <= THRESHOLD_NAIVE_REMAINDER) return naive_div_inplace(std::move(g), gd).second;
            *this -= g * (*this / g);
            return pre_inplace(gd - 1);
        }
        inline FPS& operator/=(const FPS &g) { return *this /= FPS(g); }
        inline FPS& operator%=(const FPS &g) { return *this %= FPS(g); }
        FPS& operator<<=(const int shamt) {
            this->insert(this->begin(), shamt, 0);
            return *this;
        }
        FPS& operator>>=(const int shamt) {
            if (shamt > size()) this->clear();
            else this->erase(this->begin(), this->begin() + shamt);
            return *this;
        }

        inline FPS operator+(FPS &&g) const { return FPS(*this) += std::move(g); }
        inline FPS operator-(FPS &&g) const { return FPS(*this) -= std::move(g); }
        inline FPS operator*(FPS &&g) const { return FPS(*this) *= std::move(g); }
        inline FPS operator/(FPS &&g) const { return FPS(*this) /= std::move(g); }
        inline FPS operator%(FPS &&g) const { return FPS(*this) %= std::move(g); }
        inline FPS operator+(const FPS &g) const { return FPS(*this) += g; }
        inline FPS operator+(const mint x) const { return FPS(*this) += x; }
        inline FPS operator-(const FPS &g) const { return FPS(*this) -= g; }
        inline FPS operator-(const mint x) const { return FPS(*this) -= x; }
        inline FPS operator*(const FPS &g) const { return FPS(*this) *= g; }
        inline FPS operator*(const mint x) const { return FPS(*this) *= x; }
        inline FPS operator/(const FPS &g) const { return FPS(*this) /= g; }
        inline FPS operator%(const FPS &g) const { return FPS(*this) %= g; }
        inline friend FPS operator*(const mint x, const FPS  &f) { return f * x; }
        inline friend FPS operator*(const mint x,       FPS &&f) { return f *= x; }
        inline FPS operator<<(const int shamt) { return FPS(*this) <<= shamt; }
        inline FPS operator>>(const int shamt) { return FPS(*this) >>= shamt; }

        friend bool operator==(const FPS &f, const FPS &g) {
            int n = f.size(), m = g.size();
            if (n < m) return g == f;
            for (int i = 0; i < m; ++i) if (f.unsafe_get(i) != g.unsafe_get(i)) return false;
            for (int i = m; i < n; ++i) if (f.unsafe_get(i) != 0) return false;
            return true;
        }

        FPS& diff_inplace() {
            if (this->size() == 0) return *this;
            for (int i = 1; i <= deg(); ++i) unsafe_get(i - 1) = unsafe_get(i) * i;
            this->pop_back();
            return *this;
        }
        FPS& intg_inplace() {
            int d = deg();
            ensure_deg(d + 1);
            for (int i = d; i >= 0; --i) unsafe_get(i + 1) = unsafe_get(i) * invs[i + 1];
            unsafe_get(0) = 0;
            return *this;
        }
        FPS& inv_inplace(const int max_deg) {
            FPS res { unsafe_get(0).inv() };
            for (int k = 1; k <= max_deg; k *= 2) {
                FPS tmp(this->pre(k * 2) * (res * res));
                res *= 2, res -= tmp.pre_inplace(2 * k);
            }
            return *this = std::move(res), pre_inplace(max_deg);
        }
        FPS& log_inplace(const int max_deg) {
            FPS f_inv = inv(max_deg);
            diff_inplace(), *this *= f_inv, pre_inplace(max_deg - 1), intg_inplace();
            return *this;
        }
        FPS& exp_inplace(const int max_deg) {
            FPS res {1};
            for (int k = 1; k <= max_deg; k *= 2) res *= ++(pre(k * 2) - res.log(k * 2)), res.pre_inplace(k * 2);
            return *this = std::move(res), pre_inplace(max_deg);
        }
        FPS& pow_inplace(const long long k, const int max_deg) {
            int tlz = 0;
            while (tlz <= deg() and unsafe_get(tlz) == 0) ++tlz;
            if (tlz * k > max_deg) { this->clear(); return *this; }
            *this >>= tlz;
            mint base = (*this)[0];
            *this *= base.inv(), log_inplace(max_deg), *this *= k, exp_inplace(max_deg), *this *= base.pow(k);
            return *this <<= tlz * k, pre_inplace(max_deg);
        }
        inline FPS diff() const { return FPS(*this).diff_inplace(); }
        inline FPS intg() const { return FPS(*this).intg_inplace(); }
        inline FPS inv(const int max_deg) const { return FPS(*this).inv_inplace(max_deg); }
        inline FPS log(const int max_deg) const { return FPS(*this).log_inplace(max_deg); }
        inline FPS exp(const int max_deg) const { return FPS(*this).exp_inplace(max_deg); }
        inline FPS pow(const long long k, const int max_deg) const { return FPS(*this).pow_inplace(k, max_deg); }

    private:
        static inline inv_mods<mint> invs;
        static convolution_t<mint> mult;
        inline void ensure_deg(int d) { if (deg() < d) this->resize(d + 1, 0); }
        inline const mint& unsafe_get(int i) const { return std::vector<mint>::operator[](i); }
        inline       mint& unsafe_get(int i)       { return std::vector<mint>::operator[](i); }

        std::pair<FPS, FPS&> naive_div_inplace(FPS &&g, const int gd) {
            const int k = deg() - gd;
            mint head_inv = g.unsafe_get(gd).inv();
            FPS q(k + 1);
            for (int i = k; i >= 0; --i) {
                mint div = this->unsafe_get(i + gd) * head_inv;
                q.unsafe_get(i) = div;
                for (int j = 0; j <= gd; ++j) this->unsafe_get(i + j) -= div * g.unsafe_get(j);
            }
            return {q, pre_inplace(gd - 1)};
        }
};

template <typename mint>
convolution_t<mint> FPS<mint>::mult = [](const auto &, const auto &) {
    std::cerr << "convolution function is not available." << std::endl;
    assert(false);
    return std::vector<mint>{};
};

} // namespace suisen

template <typename mint>
auto sqrt(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{})  {
    assert(false);
}
template <typename mint>
auto log(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{}) {
    return a.log(a.deg());
}
template <typename mint>
auto exp(suisen::FPS<mint> a) -> decltype(mint::mod(), mint()) {
    return a.exp(a.deg());
}
template <typename mint, typename T>
auto pow(suisen::FPS<mint> a, T b) -> decltype(mint::mod(), mint()) {
    return a.pow(b, a.deg());
}
template <typename mint>
auto inv(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{})  {
    return a.inv(a.deg());
}

namespace suisen {
template <typename mint>
std::vector<mint> multi_point_eval(const FPS<mint> &f, const std::vector<mint> &xs) {
    int m = xs.size();
    int k = 1;
    while (k < m) k <<= 1;
    std::vector<FPS<mint>> seg(2 * k);
    for (int i = 0; i < m; ++i) seg[k + i] = FPS<mint> {-xs[i], 1};
    for (int i = m; i < k; ++i) seg[k + i] = FPS<mint> {1};
    for (int i = k - 1; i> 0; --i) seg[i] = seg[i * 2] * seg[i * 2 + 1];
    seg[1] = f % seg[1];
    for (int i = 2; i < k + m; ++i) seg[i] = seg[i / 2] % seg[i];
    std::vector<mint> ys(m);
    for (int i = 0; i < m; ++i) ys[i] = seg[k + i][0];
    return ys;
}
} // namespace suisen

namespace suisen {

// O(N(logN)^2)
// return the vector p of length xs.size() s.t. p[i]=Π[j!=i](x[i]-x[j])
template <typename T>
std::vector<T> product_of_differences(const std::vector<T> &xs) {
    // f(x):=Π_i(x-x[i])
    // => f'(x)=Σ_i Π[j!=i](x-x[j])
    // => f'(x[i])=Π[j!=i](x[i]-x[j])
    const int n = xs.size();
    std::deque<FPS<T>> dq;
    for (int i = 0; i < n; ++i) dq.push_back(FPS<T>{ -xs[i], T{1} });
    while (dq.size() >= 2) {
        auto f = std::move(dq.front());
        dq.pop_front();
        auto g = std::move(dq.front());
        dq.pop_front();
        dq.push_back(f * g);
    }
    auto f = std::move(dq.front());
    f.diff_inplace();
    return multi_point_eval(f, xs);
}

// O(N(logN)^2+NlogP)
template <typename T>
T lagrange_interpolation(const std::vector<T> &xs, const std::vector<T> &ys, const T t) {
    const int n = xs.size();
    assert(int(ys.size()) == n);

    T p{1};
    for (int i = 0; i < n; ++i) p *= t - xs[i];

    std::vector<T> w = product_of_differences(xs);
    T res{0};
    for (int i = 0; i < n; ++i) {
        res += t == xs[i] ? ys[i] : ys[i] * p / (w[i] * (t - xs[i]));
    }
    return res;
}

template <typename T>
T lagrange_interpolation(const std::vector<T> &ys, const T t) {
    const int n = ys.size();
    T fac = 1;
    for (int i = 1; i < n; ++i) fac *= i;
    std::vector<T> fci(n), suf(n);
    fci[n - 1] = T(1) / fac;
    suf[n - 1] = 1;
    for (int i = n - 1; i > 0; --i) {
        fci[i - 1] = fci[i] * i;
        suf[i - 1] = suf[i] * (t - i);
    }
    T prf = 1, res = 0;
    for (int i = 0; i < n; ++i) {
        T val = ys[i] * prf * suf[i] * fci[i] * fci[n - i - 1];
        if ((n - 1 - i) & 1) {
            res -= val;
        } else {
            res += val;
        }
        prf *= t - i;
    }
    return res;
}

template <typename mint>
FPS<mint> polynomial_interpolation(const std::vector<mint> &xs, const std::vector<mint> &ys) {
    assert(xs.size() == ys.size());
    int n = xs.size();
    int k = 1;
    while (k < n) k <<= 1;
    std::vector<FPS<mint>> seg(k << 1), g(k << 1);
    for (int i = 0; i < n; ++i) seg[k + i] = FPS<mint> {-xs[i], 1};
    for (int i = n; i < k; ++i) seg[k + i] = FPS<mint> {1};
    for (int i = k - 1; i > 0; --i) {
        seg[i] = seg[i * 2] * seg[i * 2 + 1];
    }
    g[1] = std::move(seg[1].diff_inplace());
    for (int i = 1; i < k; ++i) {
        int l = 2 * i, r = l + 1;
        g[l] = g[i] % seg[l], g[r] = g[i] % seg[r];
    }
    for (int i = 0; i < n; ++i) g[k + i] = FPS<mint> {ys[i] / g[k + i][0]};
    for (int i = n; i < k; ++i) g[k + i] = FPS<mint> {0};
    for (int i = k - 1; i > 0; --i) {
        int l = 2 * i, r = l + 1;
        g[i] = g[l] * seg[r] + g[r] * seg[l];
    }
    return g[1];
}
} // namespace suisen

int main() {
    suisen::FPS<mint>::set_multiplication([](const auto &a, const auto &b) { return atcoder::convolution(a, b); });

    input(int, n);
    input(mint, x);

    vector<mint> xs(n), ys(n);
    rep(i, n) read(xs[i], ys[i]);

    vector<mint> p = product_of_differences(xs);

    mint s = 0;
    rep(i, n) s += ys[i] / p[i];

    mint prd = 1;
    rep(i, n) prd *= x - xs[i];

    mint ans = 0;
    rep(i, n) {
        mint num = x == xs[i] ? p[i] : prd / (x - xs[i]);
        ans += (n * ys[i] / p[i] - s) * num;
    }
    print(ans);

    return 0;
}