#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <chrono>
#include<functional>

using namespace std;

constexpr long long P = 998244353;
const long long mod = P;
using i64 = long long;
#define ll long long

ll start = 0;

inline long long get_time() {
    return chrono::duration_cast<chrono::milliseconds>(chrono::steady_clock().now().time_since_epoch()).count();
}

inline ll get_delta() {
    ll k = get_time() - start;
    start += k;
    return k;
}

inline void delta() {
    cout << get_delta() << "\n";
}

inline long long mul(long long a, long long b) {
    return a * b % P;
}

// assume -P <= x < 2P
inline int norm(int x) {
    if (x < 0) {
        x += P;
    }
    if (x >= P) {
        x -= P;
    }
    return x;
}

inline long long bp(long long a, int b) {
    long long res = 1;
    for (; b; b /= 2, a = mul(a, a)) {
        if (b % 2) {
            res = mul(res, a);
        }
    }
    return res;
}

template <class T>
inline T power(T a, int b) {
    T res = 1;
    for (; b; b /= 2, a *= a) {
        if (b % 2) {
            res *= a;
        }
    }
    return res;
}

struct Z {
    int x;
    inline Z(int x = 0) : x(norm(x)) {}
    int val() const {
        return x;
    }
    inline Z operator-() const {
        return Z(norm(P - x));
    }
    inline Z inv() const {
        return power(*this, P - 2);
    }
    inline Z& operator*=(const Z& rhs) {
        x = i64(x) * rhs.x % P;
        return *this;
    }
    inline Z& operator+=(const Z& rhs) {
        x = norm(x + rhs.x);
        return *this;
    }
    inline Z& operator-=(const Z& rhs) {
        x = norm(x - rhs.x);
        return *this;
    }
    inline Z& operator/=(const Z& rhs) {
        return *this *= rhs.inv();
    }
    inline friend Z operator*(const Z& lhs, const Z& rhs) {
        Z res = lhs;
        res *= rhs;
        return res;
    }
    inline friend Z operator+(const Z& lhs, const Z& rhs) {
        Z res = lhs;
        res += rhs;
        return res;
    }
    inline friend Z operator-(const Z& lhs, const Z& rhs) {
        Z res = lhs;
        res -= rhs;
        return res;
    }
    inline friend Z operator/(const Z& lhs, const Z& rhs) {
        Z res = lhs;
        res /= rhs;
        return res;
    }
};

std::vector<int> rev;
std::vector<Z> roots{ 0, 1 };
inline void dft(std::vector<Z>& a) {
    int n = a.size();

    if (int(rev.size()) != n) {
        int k = 0;
        while ((1 << k) < n) k++;
        k--;
        rev.resize(n);
        for (int i = 0; i < n; i++) {
            rev[i] = rev[i >> 1] >> 1 | (i & 1) << k;
        }
    }

    for (int i = 0; i < n; i++) {
        if (rev[i] < i) {
            std::swap(a[i], a[rev[i]]);
        }
    }
    if (int(roots.size()) < n) {
        int k = 0;
        while ((1 << k) < roots.size()) k++;
        roots.resize(n);
        while ((1 << k) < n) {
            Z e = power(Z(3), (P - 1) >> (k + 1));
            for (int i = 1 << (k - 1); i < (1 << k); i++) {
                roots[2 * i] = roots[i];
                roots[2 * i + 1] = roots[i] * e;
            }
            k++;
        }
    }
    for (int k = 1; k < n; k *= 2) {
        for (int i = 0; i < n; i += 2 * k) {
            for (int j = 0; j < k; j++) {
                Z u = a[i + j];
                Z v = a[i + j + k] * roots[k + j];
                a[i + j] = u + v;
                a[i + j + k] = u - v;
            }
        }
    }
}

inline void idft(std::vector<Z>& a) {
    int n = a.size();
    std::reverse(a.begin() + 1, a.end());
    dft(a);
    Z inv = (1 - P) / n;
    for (int i = 0; i < n; i++) {
        a[i] *= inv;
    }
}

vector <Z> longtoZ(vector <long long> a);

struct Poly {
    std::vector<Z> a;
    Poly() {}
    Poly(const std::vector<Z>& a) : a(a) {}
    Poly(const std::vector<long long>& a) : a(longtoZ(a)) {}
    Poly(const std::initializer_list<Z>& a) : a(a) {}
    inline int size() const {
        return a.size();
    }
    inline void resize(int n) {
        a.resize(n);
    }
    inline Z operator[](int idx) const {
        if (idx < 0 || idx >= size()) {
            return 0;
        }
        return a[idx];
    }
    inline Z& operator[](int idx) {
        return a[idx];
    }
    inline Poly mulxk(int k) const {
        auto b = a;
        b.insert(b.begin(), k, 0);
        return Poly(b);
    }
    inline Poly modxk(int k) const {
        k = std::min(k, size());
        return Poly(std::vector<Z>(a.begin(), a.begin() + k));
    }
    inline Poly divxk(int k) const {
        if (size() <= k) {
            return Poly();
        }
        return Poly(std::vector<Z>(a.begin() + k, a.end()));
    }
    inline friend Poly operator+(const Poly& a, const Poly& b) {
        std::vector<Z> res(std::max(a.size(), b.size()));
        for (int i = 0; i < int(res.size()); i++) {
            res[i] = a[i] + b[i];
        }
        return Poly(res);
    }
    inline friend Poly operator-(const Poly& a, const Poly& b) {
        std::vector<Z> res(std::max(a.size(), b.size()));
        for (int i = 0; i < int(res.size()); i++) {
            res[i] = a[i] - b[i];
        }
        return Poly(res);
    }
    inline friend Poly operator*(Poly a, Poly b) {
        if (a.size() == 0 || b.size() == 0) {
            return Poly();
        }
        int sz = 1, tot = a.size() + b.size() - 1;
        while (sz < tot)
            sz *= 2;
        a.a.resize(sz);
        b.a.resize(sz);
        dft(a.a);
        dft(b.a);
        for (int i = 0; i < sz; ++i) {
            a.a[i] = a[i] * b[i];
        }
        idft(a.a);
        a.resize(tot);
        return a;
    }
    inline friend Poly operator*(Z a, Poly b) {
        for (int i = 0; i < int(b.size()); i++) {
            b[i] *= a;
        }
        return b;
    }
    inline friend Poly operator*(Poly a, Z b) {
        for (int i = 0; i < int(a.size()); i++) {
            a[i] *= b;
        }
        return a;
    }
    inline Poly& operator+=(Poly b) {
        return (*this) = (*this) + b;
    }
    inline Poly& operator-=(Poly b) {
        return (*this) = (*this) - b;
    }
    inline Poly& operator*=(Poly b) {
        return (*this) = (*this) * b;
    }
    inline Poly inv(int m) const {
        Poly x{ a[0].inv() };
        int k = 1;
        while (k < m) {
            k *= 2;
            x = (x * (Poly{ 2 } - modxk(k) * x)).modxk(k);
        }
        return x.modxk(m);
    }
    inline Poly mulT(Poly b) const {
        if (b.size() == 0) {
            return Poly();
        }
        int n = b.size();
        std::reverse(b.a.begin(), b.a.end());
        return ((*this) * b).divxk(n - 1);
    }
    inline std::vector<Z> eval(std::vector<Z> x) const {
        if (size() == 0) {
            return std::vector<Z>(x.size(), 0);
        }
        if (size() < 450) {
            vector <Z> ans(x.size(), 0);
            for (int i = 0; i < x.size(); i++) {
                for (int j = size() - 1; j >= 0; j--) {
                    ans[i] *= x[i];
                    ans[i] += a[j];
                }
            }
            return ans;
        }
        const int n = std::max(int(x.size()), size());
        std::vector<Poly> q(4 * n);
        std::vector<Z> ans(x.size());
        x.resize(n);
        std::function<void(int, int, int)> build = [&](int p, int l, int r) {
            if (r - l == 1) {
                q[p] = Poly{ 1, -x[l] };
            }
            else {
                int m = (l + r) / 2;
                build(2 * p, l, m);
                build(2 * p + 1, m, r);
                q[p] = q[2 * p] * q[2 * p + 1];
            }
        };
        build(1, 0, n);
        std::function<void(int, int, int, const Poly&)> work = [&](int p, int l, int r, const Poly& num) {
            if (r - l == 1) {
                if (l < int(ans.size())) {
                    ans[l] = num[0];
                }
            }
            else {
                int m = (l + r) / 2;
                work(2 * p, l, m, num.mulT(q[2 * p + 1]).modxk(m - l));
                work(2 * p + 1, m, r, num.mulT(q[2 * p]).modxk(r - m));
            }
        };
        work(1, 0, n, mulT(q[1].inv(n)));
        return ans;
    }
};

inline vector <Z> longtoZ(vector <long long> a) {
    vector <Z> b;
    for (auto& i : a) b.push_back(Z(i));
    return b;
}

inline vector <long long> Ztolong(vector <Z> a) {
    vector <long long> b; for (auto& i : a) b.push_back(i.x);
    return b;
}

vector<long long> mult(vector<long long> a, vector<long long> b) {
    Poly p1(a);
    Poly p2(b);
    return Ztolong((p1 * p2).a);
}

vector<long long> eval(vector<long long> a, vector<long long> x) {
    return Ztolong(Poly(a).eval(longtoZ(x)));
}