#include <bits/stdc++.h>

#ifdef _MSC_VER
#  include <intrin.h>
#else
#  include <x86intrin.h>
#endif

#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;

template <typename T, typename = void>
struct rec_value_type {
    using type = T;
};
template <typename T>
struct rec_value_type<T, std::void_t<typename T::value_type>> {
    using type = typename rec_value_type<typename T::value_type>::type;
};
template <typename T>
using rec_value_type_t = typename rec_value_type<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

// __int128_t
std::ostream& operator<<(std::ostream& dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[128];
        char* d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);
        if (value < 0) {
            --d;
            *d = '-';
        }
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}
// __uint128_t
std::ostream& operator<<(std::ostream& dest, __uint128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        char buffer[128];
        char* d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[value % 10];
            value /= 10;
        } while (value != 0);
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}

// 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;
}

__int128_t parse_i128(std::string& s) {
    __int128_t ret = 0;
    for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
    if (s[0] == '-') ret = -ret;
    return ret;
}
__uint128_t parse_u128(std::string& s) {
    __uint128_t ret = 0;
    for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
    return ret;
}
// __int128_t
std::istream& operator>>(std::istream& in, __int128_t& v) {
    std::string s;
    in >> s;
    v = parse_i128(s);
    return in;
}
// __uint128_t
std::istream& operator>>(std::istream& in, __uint128_t& v) {
    std::string s;
    in >> s;
    v = parse_u128(s);
    return in;
}
// 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>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u64(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; }

// ! 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;
}

template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::string bin(T val, int bit_num = -1) {
    std::string res;
    if (bit_num >= 0) {
        for (int bit = bit_num; bit-- > 0;) res += '0' + ((val >> bit) & 1);
    } else {
        for (; val; val >>= 1) res += '0' + (val & 1);
        std::reverse(res.begin(), res.end());
    }
    return res;
}

template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_low_to_high(T val, T base = 10) {
    std::vector<T> res;
    for (; val; val /= base) res.push_back(val % base);
    if (res.empty()) res.push_back(T{ 0 });
    return res;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_high_to_low(T val, T base = 10) {
    auto res = digits_low_to_high(val, base);
    std::reverse(res.begin(), res.end());
    return res;
}

template <typename T>
std::string join(const std::vector<T>& v, const std::string& sep, const std::string& end) {
    std::ostringstream ss;
    for (auto it = v.begin(); it != v.end();) {
        ss << *it;
        if (++it != v.end()) ss << sep;
    }
    ss << end;
    return ss.str();
}

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

#include <cmath>
#include <vector>

#include <optional>

namespace suisen {
/**
 * refernce: https://37zigen.com/tonelli-shanks-algorithm/
 * calculates x s.t. x^2 = a mod p in O((log p)^2).
 */
template <typename mint>
std::optional<mint> optional_sqrt(mint a) {
    static int p = mint::mod();
    if (a == 0) return std::make_optional(0);
    if (p == 2) return std::make_optional(a);
    if (a.pow((p - 1) / 2) != 1) return std::nullopt;
    mint b = 1;
    while (b.pow((p - 1) / 2) == 1) ++b;
    static int tlz = __builtin_ctz(p - 1), q = (p - 1) >> tlz;
    mint x = a.pow((q + 1) / 2);
    b = b.pow(q);
    for (int shift = 2; x * x != a; ++shift) {
        mint e = a.inv() * x * x;
        if (e.pow(1 << (tlz - shift)) != 1) x *= b;
        b *= b;
    }
    return std::make_optional(x);
}

};

/**
 * calculates x s.t. x^2 = a mod p in O((log p)^2).
 * if not exists, raises runtime error.
 */
template <typename mint>
auto sqrt(mint a) -> decltype(mint::mod(), mint()) {
    return *suisen::optional_sqrt(a);
}
template <typename mint>
auto log(mint a) -> decltype(mint::mod(), mint())  {
    assert(a == 1);
    return 0;
}
template <typename mint>
auto exp(mint a) -> decltype(mint::mod(), mint())  {
    assert(a == 0);
    return 1;
}
template <typename mint, typename T>
auto pow(mint a, T b) -> decltype(mint::mod(), mint())  {
    return a.pow(b);
}
template <typename mint>
auto inv(mint a) -> decltype(mint::mod(), mint()) {
    return a.inv();
}

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 T>
    struct FPSNaive : std::vector<T> {
        static inline int MAX_DEG = std::numeric_limits<int>::max() / 2;

        using value_type = T;
        using element_type = rec_value_type_t<T>;
        using std::vector<value_type>::vector;

        FPSNaive(const std::initializer_list<value_type> l) : std::vector<value_type>::vector(l) {}

        static void set_max_deg(int max_deg) {
            FPSNaive<T>::MAX_DEG = max_deg;
        }

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

        int size() const {
            return std::vector<value_type>::size();
        }
        int deg() const {
            return size() - 1;
        }
        int normalize() {
            while (size() and this->back() == value_type{ 0 }) this->pop_back();
            return deg();
        }
        FPSNaive& cut_inplace(int max_deg) {
            if (deg() > max_deg) this->resize(std::max(0, max_deg + 1));
            return *this;
        }
        FPSNaive cut(int max_deg) const {
            return FPSNaive(*this).cut_inplace(max_deg);
        }

        FPSNaive operator+() const {
            return FPSNaive(*this);
        }
        FPSNaive operator-() const {
            FPSNaive f(*this);
            for (auto& e : f) e = -e;
            return f;
        }
        FPSNaive& operator++() { return ++(*this)[0], * this; }
        FPSNaive& operator--() { return --(*this)[0], * this; }
        FPSNaive& operator+=(const value_type x) { return (*this)[0] += x, *this; }
        FPSNaive& operator-=(const value_type x) { return (*this)[0] -= x, *this; }
        FPSNaive& operator+=(const FPSNaive& g) {
            ensure_deg(g.deg());
            for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) += g.unsafe_get(i);
            return *this;
        }
        FPSNaive& operator-=(const FPSNaive& g) {
            ensure_deg(g.deg());
            for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) -= g.unsafe_get(i);
            return *this;
        }
        FPSNaive& operator*=(const FPSNaive& g) { return *this = *this * g; }
        FPSNaive& operator*=(const value_type x) {
            for (auto& e : *this) e *= x;
            return *this;
        }
        FPSNaive& operator/=(const FPSNaive& g) { return *this = *this / g; }
        FPSNaive& operator%=(const FPSNaive& g) { return *this = *this % g; }
        FPSNaive& operator<<=(const int shamt) {
            this->insert(this->begin(), shamt, value_type { 0 });
            return *this;
        }
        FPSNaive& operator>>=(const int shamt) {
            if (shamt > size()) this->clear();
            else this->erase(this->begin(), this->begin() + shamt);
            return *this;
        }

        friend FPSNaive operator+(FPSNaive f, const FPSNaive& g)   { f += g; return f; }
        friend FPSNaive operator+(FPSNaive f, const value_type &x) { f += x; return f; }
        friend FPSNaive operator-(FPSNaive f, const FPSNaive& g)   { f -= g; return f; }
        friend FPSNaive operator-(FPSNaive f, const value_type &x) { f -= x; return f; }
        friend FPSNaive operator*(const FPSNaive &f, const FPSNaive& g) {
            if (f.empty() or g.empty()) return FPSNaive{};
            const int n = f.size(), m = g.size();
            FPSNaive h(std::min(MAX_DEG + 1, n + m - 1));
            for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) {
                if (i + j > MAX_DEG) break;
                h.unsafe_get(i + j) += f.unsafe_get(i) * g.unsafe_get(j);
            }
            return h;
        }
        friend FPSNaive operator*(FPSNaive f, const value_type &x) { f *= x; return f; }
        friend FPSNaive operator/(FPSNaive f, FPSNaive g) { return std::move(div_mod(std::move(f), std::move(g)).first); }
        friend FPSNaive operator%(FPSNaive f, FPSNaive g) { return std::move(div_mod(std::move(f), std::move(g)).second); }
        friend FPSNaive operator*(const value_type x, FPSNaive f) { f *= x; return f; }
        friend FPSNaive operator<<(FPSNaive f, const int shamt)   { f <<= shamt; return f; }
        friend FPSNaive operator>>(FPSNaive f, const int shamt)   { f >>= shamt; return f; }

        friend std::pair<FPSNaive, FPSNaive> div_mod(FPSNaive f, FPSNaive g) {
            const int fd = f.normalize(), gd = g.normalize();
            assert(gd >= 0);
            if (fd < gd) return { FPSNaive{}, f };
            if (gd == 0) return { f *= g.unsafe_get(0).inv(), FPSNaive{} };
            const int k = f.deg() - gd;
            value_type head_inv = g.unsafe_get(gd).inv();
            FPSNaive q(k + 1);
            for (int i = k; i >= 0; --i) {
                value_type div = f.unsafe_get(i + gd) * head_inv;
                q.unsafe_get(i) = div;
                for (int j = 0; j <= gd; ++j) f.unsafe_get(i + j) -= div * g.unsafe_get(j);
            }
            return { q, f.cut_inplace(gd - 1) };
        }

        friend bool operator==(const FPSNaive& f, const FPSNaive& g) {
            const 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;
        }
        friend bool operator!=(const FPSNaive& f, const FPSNaive& g) {
            return not (f == g);
        }

        FPSNaive mul(const FPSNaive& g, int max_deg) const {
            if (this->empty() or g.empty()) return FPSNaive{};
            const int n = size(), m = g.size();
            FPSNaive h(std::min(max_deg + 1, n + m - 1));
            for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) {
                if (i + j > max_deg) break;
                h.unsafe_get(i + j) += unsafe_get(i) * g.unsafe_get(j);
            }
            return h;
        }
        FPSNaive diff() const {
            if (this->empty()) return {};
            FPSNaive g(size() - 1);
            for (int i = 1; i <= deg(); ++i) g.unsafe_get(i - 1) = unsafe_get(i) * i;
            return g;
        }
        FPSNaive intg() const {
            const int n = size();
            FPSNaive g(n + 1);
            for (int i = 0; i < n; ++i) g.unsafe_get(i + 1) = unsafe_get(i) * invs[i + 1];
            if (g.deg() > MAX_DEG) g.cut_inplace(MAX_DEG);
            return g;
        }
        FPSNaive inv(int max_deg) const {
            FPSNaive g(max_deg + 1);
            const value_type inv_f0 = ::inv(unsafe_get(0));
            g.unsafe_get(0) = inv_f0;
            for (int i = 1; i <= max_deg; ++i) {
                for (int j = 1; j <= i; ++j) g.unsafe_get(i) -= g.unsafe_get(i - j) * (*this)[j];
                g.unsafe_get(i) *= inv_f0;
            }
            return g;
        }
        FPSNaive exp(int max_deg) const {
            assert(unsafe_get(0) == value_type{ 0 });
            FPSNaive g(max_deg + 1);
            g.unsafe_get(0) = value_type{ 1 };
            for (int i = 1; i <= max_deg; ++i) {
                for (int j = 1; j <= i; ++j) g.unsafe_get(i) += j * g.unsafe_get(i - j) * (*this)[j];
                g.unsafe_get(i) *= invs[i];
            }
            return g;
        }
        FPSNaive log(int max_deg) const {
            assert(unsafe_get(0) == value_type{ 1 });
            FPSNaive g(max_deg + 1);
            g.unsafe_get(0) = value_type{ 0 };
            for (int i = 1; i <= max_deg; ++i) {
                g.unsafe_get(i) = i * (*this)[i];
                for (int j = 1; j < i; ++j) g.unsafe_get(i) -= (i - j) * g.unsafe_get(i - j) * (*this)[j];
                g.unsafe_get(i) *= invs[i];
            }
            return g;
        }
        FPSNaive pow(const long long k, int max_deg) const {
            if (k == 0) return { value_type{ 1 } };
            int z = 0;
            while (z < size() and unsafe_get(z) == value_type{ 0 }) ++z;
            if (z >= max_deg / k + 1) return FPSNaive{};
            const int d = max_deg - z * k;

            FPSNaive g(d + 1);
            const value_type inv_f0 = ::inv(unsafe_get(z));
            g.unsafe_get(0) = unsafe_get(z).pow(k);
            for (int i = 1; i <= d; ++i) {
                for (int j = 1; j <= i; ++j) g.unsafe_get(i) += (element_type{ k } * j - (i - j)) * g.unsafe_get(i - j) * (*this)[z + j];
                g.unsafe_get(i) *= inv_f0 * invs[i];
            }
            g <<= z * k;
            return g;
        }

        FPSNaive sqrt(int max_deg) const {
            int dl = 0;
            while (dl < size() and unsafe_get(dl) == value_type{ 0 }) ++dl;
            if (dl == size()) return FPSNaive{};
            if (dl & 1) assert(false);

            const int d = max_deg - dl / 2;

            FPSNaive g(d + 1);
            g.unsafe_get(0) = ::sqrt((*this)[dl]);
            value_type inv_2g0 = ::inv(2 * g.unsafe_get(0));
            for (int i = 1; i <= d; ++i) {
                g.unsafe_get(i) = unsafe_get(dl + i);
                for (int j = 1; j < i; ++j) g.unsafe_get(i) -= g.unsafe_get(j) * g.unsafe_get(i - j);
                g.unsafe_get(i) *= inv_2g0;
            }
            g <<= dl / 2;
            return g;
        }

        value_type eval(value_type x) const {
            value_type y = 0;
            for (int i = size() - 1; i >= 0; --i) y = y * x + unsafe_get(i);
            return y;
        }

    private:
        static inline inv_mods<element_type> invs;

        void ensure_deg(int d) {
            if (deg() < d) this->resize(d + 1, value_type{ 0 });
        }
        const value_type& unsafe_get(int i) const {
            return std::vector<value_type>::operator[](i);
        }
        value_type& unsafe_get(int i) {
            return std::vector<value_type>::operator[](i);
        }
    };
} // namespace suisen

template <typename mint>
auto sqrt(suisen::FPSNaive<mint> a) -> decltype(mint::mod(), suisen::FPSNaive<mint>{}) {
    return a.sqrt(suisen::FPSNaive<mint>::MAX_DEG == std::numeric_limits<int>::max() / 2 ? suisen::FPSNaive<mint>::MAX_DEG : a.deg());
}
template <typename mint>
auto log(suisen::FPSNaive<mint> a) -> decltype(mint::mod(), suisen::FPSNaive<mint>{}) {
    return a.log(suisen::FPSNaive<mint>::MAX_DEG == std::numeric_limits<int>::max() / 2 ? suisen::FPSNaive<mint>::MAX_DEG : a.deg());
}
template <typename mint>
auto exp(suisen::FPSNaive<mint> a) -> decltype(mint::mod(), suisen::FPSNaive<mint>{}) {
    return a.exp(suisen::FPSNaive<mint>::MAX_DEG == std::numeric_limits<int>::max() / 2 ? suisen::FPSNaive<mint>::MAX_DEG : a.deg());
}
template <typename mint, typename T>
auto pow(suisen::FPSNaive<mint> a, T b) -> decltype(mint::mod(), suisen::FPSNaive<mint>{}) {
    return a.pow(b, suisen::FPSNaive<mint>::MAX_DEG == std::numeric_limits<int>::max() / 2 ? suisen::FPSNaive<mint>::MAX_DEG : a.deg());
}
template <typename mint>
auto inv(suisen::FPSNaive<mint> a) -> decltype(mint::mod(), suisen::FPSNaive<mint>{}) {
    return a.inv(suisen::FPSNaive<mint>::MAX_DEG == std::numeric_limits<int>::max() / 2 ? suisen::FPSNaive<mint>::MAX_DEG : a.deg());
}

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

    template <typename mint>
    struct FPS : public std::vector<mint> {
        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;
        }

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

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

        FPS operator+() const { return FPS(*this); }
        FPS operator-() const {
            FPS f(*this);
            for (auto& e : f) e = mint::mod() - e;
            return f;
        }
        FPS& operator++() { ++(*this)[0]; return *this; }
        FPS& operator--() { --(*this)[0]; return *this; }
        FPS& operator+=(const mint x) { (*this)[0] += x; return *this; }
        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;
        }
        FPS& operator*=(const FPS& g) { return *this = FPS<mint>::mult(*this, g); }
        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);
        }
        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;
        }

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

        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) {
            if (max_deg <= 60) return *this = FPSNaive<mint>(this->begin(), this->end()).inv(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) {
            if (max_deg <= 60) return *this = FPSNaive<mint>(this->begin(), this->end()).log(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) {
            if (max_deg <= 60) return *this = FPSNaive<mint>(this->begin(), this->end()).exp(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) {
            if (max_deg <= 60) return *this = FPSNaive<mint>(this->begin(), this->end()).pow(k, 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);
        }
        FPS diff() const { FPS f{ *this }; f.diff_inplace(); return f; }
        FPS intg() const { FPS f{ *this }; f.intg_inplace(); return f; }
        FPS inv(const int max_deg) const { FPS f{ *this }; f.inv_inplace(max_deg); return f; }
        FPS log(const int max_deg) const { FPS f{ *this }; f.log_inplace(max_deg); return f; }
        FPS exp(const int max_deg) const { FPS f{ *this }; f.exp_inplace(max_deg); return f; }
        FPS pow(const long long k, const int max_deg) const { FPS f{ *this }; f.pow_inplace(k, max_deg); return f; }

        mint eval(mint x) const {
            mint y = 0;
            for (int i = size() - 1; i >= 0; --i) y = y * x + unsafe_get(i);
            return y;
        }

    private:
        static inline inv_mods<mint> invs;
        static convolution_t<mint> mult;
        void ensure_deg(int d) { if (deg() < d) this->resize(d + 1, 0); }
        const mint& unsafe_get(int i) const { return std::vector<mint>::operator[](i); }
        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(), suisen::FPS<mint>{}) {
    return a.exp(a.deg());
}
template <typename mint, typename T>
auto pow(suisen::FPS<mint> a, T b) -> decltype(mint::mod(), suisen::FPS<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());
}

mint pow(mint a, int k) {
    mint res = a.pow(abs(k));
    return k >= 0 ? res : res.inv();
}

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

    input(int, n, k);
    FPS<mint> f(n + 1);
    rep(i, n) {
        read(f[i + 1]);
    }
    FPS<mint> df = f.diff();

    if (df == FPS<mint>{}) {
        print(vector<mint>(n, 0));
        return 0;
    }
    int z = 0;
    while (df[z] == 0) ++z;

    FPS<mint> g;
    if (k >= 0) {
        auto h = (f >> z) * (df >> z).inv(n);
        h.resize(n + 1);

        g = (FPS<mint>{1} - f).inv(n);
        loop(k) {
            g = g.diff() * h;
            g.resize(n + 1);
        }
    } else {
        auto h = (df >> z) * (f >> (z + 1)).inv(n);
        h.resize(n + 1);

        g = df * (FPS<mint>{1} - f).inv(n);
        g.resize(n);
        g.intg_inplace();
        loop(-k - 1) {
            g *= h;
            g.resize(n + 1);
            g >>= 1;
            g.intg_inplace();
        }
    }
    g.erase(g.begin());
    print(g);

    return 0;
}