#line 1 "library-cpp/other/template.hpp"
// clang-format off
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using maxheap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vector<T>>;
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP0(n) for (auto minato = decay_t<decltype(n)>{}; minato < (n); ++minato)
#define REP1(i, n) for (auto i = decay_t<decltype(n)>{}; (i) < (n); (i)++)
#define REP2(i, l, r) for (auto i = (l); (i) < (r); (i)++)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, name, ...) name
#define RREP1(i, n) for (auto i = (n) - 1; (i) >= decay_t<decltype(n)>{}; (i)--)
#define RREP2(i, l, r) for (auto i = (r) - 1; (i) >= (l); (i)--)
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP2, RREP1)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
template <class Container> int SZ(const Container& v) { return int(v.size()); }
template <class T> void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template <class T> T MAX(const vector<T>& v) { return *max_element(v.begin(), v.end()); }
template <class T> T MIN(const vector<T>& v) { return *min_element(v.begin(), v.end()); }
template <class T> T SUM(const vector<T>& v) { return accumulate(v.begin(), v.end(), T(0)); }
template <class T> T ABS(T x) { return max(x, -x); }
long long floor_div(long long n, long long d) { return n / d - ((n ^ d) < 0 && n % d); }
template <class T1, class T2> bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }
template <class T1, class T2> bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }
int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
int popcount(ull x) { return __builtin_popcountll(x); }
int kthbit(ull x, int k) { return (x >> k) & 1; }
constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; }
template <typename S> void rearrange(const vector<S>& id) { (void)id; }
template <typename S, typename T> void rearrange_exec(const vector<S>& id, vector<T>& v) { vector<T> w(v.size()); for (size_t i = 0; i < id.size(); i++) { w[i] = v[id[i]]; } v.swap(w); }
template <typename S, typename Head, typename... Tail> void rearrange(const vector<S>& id, Head& a, Tail& ...tail) { rearrange_exec(id, a); rearrange(id, tail...); }
istream& operator>>(istream& is, __int128_t& x) {
    x = 0;
    string s;
    is >> s;
    int n = int(s.size()), it = 0;
    if (s[0] == '-') it++;
    for (; it < n; it++) x = (x * 10 + s[it] - '0');
    if (s[0] == '-') x = -x;
    return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
    if (x == 0) return os << 0;
    if (x < 0) os << '-', x = -x;
    deque<int> deq;
    while (x) deq.emplace_front(x % 10), x /= 10;
    for (int e : deq) os << e;
    return os;
}
template <class T> vector<T> &operator++(vector<T>& v) { for (auto& e : v) { e++; } return v;} 
template <class T> vector<T> operator++(vector<T>& v, int) { auto res = v; for (auto& e : v) { e++; } return res; }
template <class T> vector<T> &operator--(vector<T>& v) { for (auto& e : v) { e--; } return v; }
template <class T> vector<T> operator--(vector<T>& v, int) { auto res = v; for (auto& e : v) { e--; } return res; }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x) { return pair<T1, T2>(-x.first, -x.second); }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first - y.first, x.second - y.second); }
template <class T1, class T2> pair<T1, T2> operator+(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first + y.first, x.second + y.second); }
template <class T1, class T2> pair<T1, T2> operator+=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l + r; }
template <class T1, class T2> pair<T1, T2> operator-=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l - r; }
constexpr char ln = '\n';
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
void YES(bool t = true) { cout << YESNO[t] << "\n"; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = true) { cout << YesNo[t] << "\n"; }
void No(bool t = 1) { Yes(!t); }
template <class T> void drop(T x) { cout << x << "\n"; exit(0); }
#define INT(...)     \
    int __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    IN(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    IN(__VA_ARGS__)
#define CHR(...)      \
    char __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LDB(...)             \
    long double __VA_ARGS__; \
    IN(__VA_ARGS__)
#define VEC(type, name, size) \
    vector<type> name(size);  \
    IN(name)
#define VEC2(type, name1, name2, size)     \
    vector<type> name1(size), name2(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size)           \
    vector<type> name1(size), name2(size), name3(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size)                 \
    vector<type> name1(size), name2(size), name3(size), name4(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, N, M)                       \
    vector<vector<type>> name(N, vector<type>(M)); \
    IN(name)
template <class T> void scan(T& a) { cin >> a; }
template <class T> void scan(vector<T>& a) { for (auto& i : a) scan(i); }
void IN() {}
template <class Head, class... Tail> void IN(Head& head, Tail&... tail) { scan(head); IN(tail...); }
std::vector<std::vector<int>> read_graph(int N, int M) {
    std::vector<std::vector<int>> g(N);
    for (int i = 0; i < M; i++) {
        int a, b;
        cin >> a >> b;
        a--, b--;
        g[a].emplace_back(b);
        g[b].emplace_back(a);
    }
    return g;
}
std::vector<std::vector<int>> read_tree(int N) { return read_graph(N, N - 1); }
void print() { cout << "\n"; }
template <class T> void print(const vector<T>& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << *it; } print(); }
template <class T, class... Args> void print(const T& x, const Args& ... args) { cout << x; if (sizeof...(Args)) cout << " "; print(args...); }
#ifdef MINATO_LOCAL
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p);
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t);
template <class T> ostream& operator<<(ostream& os, vector<T> v);
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a);
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]);
template <class Key> ostream& operator<<(ostream& os, set<Key> s);
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp);
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s);
template <class T> ostream& operator<<(ostream& os, queue<T> q);
template <class T> ostream& operator<<(ostream& os, deque<T> q);
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q);
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q);
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <size_t N, class TUPLE> void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; }
template <size_t N, class TUPLE, class T, class ...Args> void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get<N>(t); debug_tuple<N + 1, TUPLE, Args...>(os, t); }
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t) { os << "("; debug_tuple<0, tuple<Args...>, Args...>(os, t); return os << ")"; }
string debug_delim(int& i) { return i++ == 0 ? "" : ", "; }
#define debug_embrace(x) { int i = 0; os << "{";  { x } return os << "}"; }
template <class T> ostream& operator<<(ostream& os, vector<T> v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class Key> ostream& operator<<(ostream& os, set<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) }
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class T> ostream& operator<<(ostream& os, queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) }
template <class T> ostream& operator<<(ostream& os, deque<T> q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
void debug_out() { cerr << endl; }
template <class T, class... Args> void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); }
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// clang-format on
#line 2 "library-cpp/mod/FormalPowerSeriesNTTFriendly.hpp"

#line 8 "library-cpp/mod/FormalPowerSeriesNTTFriendly.hpp"

#include <atcoder/convolution>

template <typename M, int SPARSE = 10>
struct FormalPowerSeriesNTTFriendly : std::vector<M> {
    using std::vector<M>::vector;
    using FPS = FormalPowerSeriesNTTFriendly;

    FPS static read(int n) {
        FPS ret(n);
        for (int i = 0; i < n; i++) {
            long long x;
            std::cin >> x;
            ret[i] = x;
        }
        return ret;
    }

    M freq(int p) const {
        return p < (int)this->size() ? (*this)[p] : M(0);
    }

    void shrink() {
        while (!this->empty() and this->back().val() == 0) this->pop_back();
    }

    FPS pre(int le) const {
        return FPS(this->begin(),
                   this->begin() + std::min((int)this->size(), le));
    }

    FPS rev() const {
        FPS ret(*this);
        std::reverse(ret.begin(), ret.end());
        return ret;
    }

    int count_nonzero() const {
        return std::count_if(this->begin(), this->end(),
                             [](M x) { return x.val() != 0; });
    }

    std::vector<std::pair<int, M>> get_sparse() const {
        std::vector<std::pair<int, M>> ret;
        for (size_t i = 0; i < this->size(); i++) {
            if ((*this)[i].val() != 0) ret.emplace_back(i, (*this)[i]);
        }
        return ret;
    }

    FPS operator>>(int s) const {
        if ((int)this->size() <= s) return {};
        return FPS(this->begin() + s, this->end());
    }

    FPS operator<<(int s) const {
        if (this->empty()) return {};
        FPS ret(*this);
        ret.insert(ret.begin(), s, M(0));
        return ret;
    }

    FPS& operator+=(const FPS& r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (size_t i = 0; i < r.size(); i++) (*this)[i] += r[i];
        shrink();
        return *this;
    }

    FPS& operator+=(const M& v) {
        if (this->empty()) this->resize(1);
        (*this)[0] += v;
        shrink();
        return *this;
    }

    FPS& operator-=(const FPS& r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < int(r.size()); i++) (*this)[i] -= r[i];
        shrink();
        return *this;
    }

    FPS& operator-=(const M& v) {
        if (this->empty()) this->resize(1);
        (*this)[0] -= v;
        shrink();
        return *this;
    }

    FPS& operator*=(const FPS& r) {
        const int z = r.count_nonzero();
        if (z == 0) {
            this->clear();
            return *this;
        }
        if (z <= SPARSE) {
            auto sparse = r.get_sparse();
            return *this *= sparse;
        }
        auto res = atcoder::convolution(*this, r);
        return *this = {res.begin(), res.end()};
    }

    FPS& operator*=(const M& v) {
        for (auto& x : (*this)) x *= v;
        shrink();
        return *this;
    }

    FPS& operator*=(const std::vector<std::pair<int, M>>& r) {
        assert(!r.empty());
        const int m = r.back().first;
        FPS ret(this->size() + m);
        for (int i = 0; i < (int)this->size(); i++) {
            for (const auto& [j, c] : r) {
                ret[i + j] += (*this)[i] * c;
            }
        }
        ret.shrink();
        return *this = ret;
    }

    FPS& operator/=(const FPS& r) {
        if (this->size() < r.size()) {
            this->clear();
            return *this;
        }
        const int z = r.count_nonzero();
        assert(z != 0);
        if (z <= SPARSE) {
            auto sparse = r.get_sparse();
            return *this /= sparse;
        }
        int n = this->size() - r.size() + 1;
        return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev();
    }

    FPS& operator/=(const M& v) {
        assert(v.val() != 0);
        auto vinv = v.inv();
        for (auto& x : (*this)) x *= vinv;
        return *this;
    }

    FPS& operator/=(const std::vector<std::pair<int, M>>& r) {
        assert(!r.empty());
        auto [j0, c0] = r.front();
        assert(j0 == 0 && c0.val() != 0);
        auto ic = c0.inv();
        FPS ret(this->size());
        for (int i = 0; i < (int)this->size(); i++) {
            for (const auto& [j, c] : r) {
                if (j >= 1 && j <= i) {
                    ret[i] -= ret[i - j] * c;
                }
            }
            ret[i] += (*this)[i];
            ret[i] *= ic;
        }
        ret.shrink();
        return *this = ret;
    }

    FPS& operator%=(const FPS& r) {
        *this -= *this / r * r;
        shrink();
        return *this;
    }

    FPS operator+(const FPS& r) const {
        return FPS(*this) += r;
    }

    FPS operator+(const M& v) const {
        return FPS(*this) += v;
    }

    FPS operator-(const FPS& r) const {
        return FPS(*this) -= r;
    }

    FPS operator-(const M& v) const {
        return FPS(*this) -= v;
    }

    FPS operator*(const FPS& r) const {
        return FPS(*this) *= r;
    }

    FPS operator*(const M& v) const {
        return FPS(*this) *= v;
    }

    FPS operator/(const FPS& r) const {
        return FPS(*this) /= r;
    }

    FPS operator%(const FPS& r) const {
        return FPS(*this) %= r;
    }

    FPS operator-() const {
        FPS ret = *this;
        for (auto& v : ret) v = -v;
        return ret;
    }

    FPS differential() const {
        const int n = (int)this->size();
        FPS ret(std::max(0, n - 1));
        for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * M(i);
        return ret;
    }

    FPS integral() const {
        const int n = (int)this->size();
        FPS ret(n + 1);
        ret[0] = M(0);
        if (n > 0) ret[1] = M(1);
        auto mod = M::mod();
        for (int i = 2; i <= n; i++) ret[i] = -ret[mod % i] * (mod / i);
        for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
        return ret;
    }

    FPS inv(int deg = -1) const {
        assert((*this)[0] != M(0));
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        FPS ret{(*this)[0].inv()};
        ret.reserve(deg);
        for (int d = 1; d < deg; d <<= 1) {
            FPS f(d << 1), g(d << 1);
            std::copy(this->begin(), this->begin() + std::min(n, d << 1),
                      f.begin());
            std::copy(ret.begin(), ret.end(), g.begin());
            atcoder::internal::butterfly(f);
            atcoder::internal::butterfly(g);
            for (int i = 0; i < (d << 1); i++) f[i] *= g[i];
            atcoder::internal::butterfly_inv(f);
            std::fill(f.begin(), f.begin() + d, M(0));
            atcoder::internal::butterfly(f);
            for (int i = 0; i < (d << 1); i++) f[i] *= g[i];
            atcoder::internal::butterfly_inv(f);
            M iz = M(d << 1).inv();
            iz *= -iz;
            for (int i = d; i < std::min(d << 1, deg); i++)
                ret.push_back(f[i] * iz);
        }
        return ret.pre(deg);
    }

    FPS log(int deg = -1) const {
        assert((*this)[0] == M(1));
        if (deg == -1) deg = (int)this->size();
        return (differential() * inv(deg)).pre(deg - 1).integral();
    }

    FPS sqrt(const std::function<M(M)>& get_sqrt, int deg = -1) const {
        const int n = this->size();
        if (deg == -1) deg = n;
        if (this->empty()) return FPS(deg, 0);
        if ((*this)[0] == M(0)) {
            for (int i = 1; i < n; i++) {
                if ((*this)[i] != M(0)) {
                    if (i & 1) return {};
                    if (deg - i / 2 <= 0) break;
                    auto ret = (*this >> i).sqrt(get_sqrt, deg - i / 2);
                    if (ret.empty()) return {};
                    ret = ret << (i / 2);
                    if ((int)ret.size() < deg) ret.resize(deg, M(0));
                    return ret;
                }
            }
            return FPS(deg, M(0));
        }
        auto sqrtf0 = M(get_sqrt((*this)[0]));
        if (sqrtf0 * sqrtf0 != (*this)[0]) return {};
        FPS ret{sqrtf0};
        M inv2 = M(2).inv();
        for (int i = 1; i < deg; i <<= 1)
            ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
        return ret.pre(deg);
    }

    FPS exp(int deg = -1) const {
        assert(this->empty() or (*this)[0] == M(0));
        if (this->size() <= 1) return {M(1)};
        if (deg == -1) deg = (int)this->size();
        FPS inv;
        inv.reserve(deg + 1);
        inv.push_back(M(0));
        inv.push_back(M(1));
        auto inplace_integral = [&](FPS& F) -> void {
            const int n = (int)F.size();
            auto mod = M::mod();
            while ((int)inv.size() <= n) {
                int i = inv.size();
                inv.push_back(-inv[mod % i] * (mod / i));
            }
            F.insert(F.begin(), M(0));
            for (int i = 1; i <= n; i++) F[i] *= inv[i];
        };
        auto inplace_differential = [](FPS& F) -> void {
            if (F.empty()) return;
            F.erase(F.begin());
            for (size_t i = 0; i < F.size(); i++) F[i] *= M(i + 1);
        };
        FPS f{1, (*this)[1]}, g{M(1)}, g_fft{M(1), M(1)};
        for (int m = 2; m < deg; m <<= 1) {
            const M iz1 = M(m).inv(), iz2 = M(m << 1).inv();
            auto f_fft = f;
            f_fft.resize(m << 1);
            atcoder::internal::butterfly(f_fft);
            {
                FPS _g(m);
                for (int i = 0; i < m; i++) _g[i] = f_fft[i] * g_fft[i];
                atcoder::internal::butterfly_inv(_g);
                std::fill(_g.begin(), _g.begin() + (m >> 1), M(0));
                atcoder::internal::butterfly(_g);
                for (int i = 0; i < m; i++) _g[i] *= -g_fft[i] * iz1 * iz1;
                atcoder::internal::butterfly_inv(_g);
                g.insert(g.end(), _g.begin() + (m >> 1), _g.end());

                g_fft = g;
                g_fft.resize(m << 1);
                atcoder::internal::butterfly(g_fft);
            }
            FPS x(this->begin(),
                  this->begin() + std::min((int)this->size(), m));
            {
                x.resize(m);
                inplace_differential(x);
                x.push_back(M(0));
                atcoder::internal::butterfly(x);
            }
            {
                for (int i = 0; i < m; i++) x[i] *= f_fft[i] * iz1;
                atcoder::internal::butterfly_inv(x);
            }
            {
                x -= f.differential();
                x.resize(m << 1);
                for (int i = 0; i < m - 1; i++) x[m + i] = x[i], x[i] = M(0);
                atcoder::internal::butterfly(x);
                for (int i = 0; i < (m << 1); i++) x[i] *= g_fft[i] * iz2;
                atcoder::internal::butterfly_inv(x);
            }
            {
                x.pop_back();
                inplace_integral(x);
                for (int i = m; i < std::min((int)this->size(), m << 1); i++)
                    x[i] += (*this)[i];
                std::fill(x.begin(), x.begin() + m, M(0));
            }
            {
                atcoder::internal::butterfly(x);
                for (int i = 0; i < (m << 1); i++) x[i] *= f_fft[i] * iz2;
                atcoder::internal::butterfly_inv(x);
                f.insert(f.end(), x.begin() + m, x.end());
            }
        }
        return FPS{f.begin(), f.begin() + deg};
    }

    FPS pow(int64_t k, int deg = -1) const {
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        if (k == 0) {
            auto res = FPS(deg, M(0));
            res[0] = M(1);
            return res;
        }
        for (int i = 0; i < n; i++) {
            if ((*this)[i] != M(0)) {
                if (i >= (deg + k - 1) / k) return FPS(deg, M(0));
                M rev = (*this)[i].inv();
                FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg) *
                          ((*this)[i].pow(k));
                ret = (ret << (i * k)).pre(deg);
                if ((int)ret.size() < deg) ret.resize(deg, M(0));
                return ret;
            }
        }
        return FPS(deg, M(0));
    }

    M eval(M x) const {
        M ret = 0, w = 1;
        for (const auto& v : *this) ret += w * v, w *= x;
        return ret;
    }
};

template <class M, int SPARSE>
void print(const FormalPowerSeriesNTTFriendly<M, SPARSE>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        if (i) std::cout << " ";
        std::cout << v[i].val();
    }
    cout << "\n";
}
#line 3 "G.cpp"
#include <atcoder/modint>
using mint = atcoder::modint998244353;
using FPS = FormalPowerSeriesNTTFriendly<mint>;
void solve() {
    INT(P1, P2, Q1, Q2, T);
    mint P = mint(P1) / P2;
    mint Q = mint(Q1) / Q2;

    vec<mint> QX(T + 1);
    rep(i, T + 1) {
        QX[i] = Q.pow(1LL * (i + 1) * i / 2);
    }
    FPS f(T + 1), g(T + 1);
    f[0] = 1;
    rep(i, 1, T + 1) {
        f[i] -= QX[i - 1] * P;
    }
    rep(i, T + 1) {
        g[i] = QX[i];
    }
    auto h = f.inv() * g;
    mint ans = h.freq(T);
    print(ans.val());
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(7);

    int T = 1;
    // cin >> T;
    for (int test_case = 1; test_case <= T; test_case++) {
        // debug(test_case);
        solve();
    }
}