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

// #include <atcoder/all>
#include <bits/stdc++.h>

using namespace std;
// using namespace atcoder;

// #define _GLIBCXX_DEBUG

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                        \
    cerr << #v << ":";                                      \
    for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \
        cerr << " " << v[iiiiiiii];                         \
    cerr << endl;
#define DEBUG_MAT(v)                                \
    cerr << #v << endl;                             \
    for (int iv = 0; iv < v.size(); iv++) {         \
        for (int jv = 0; jv < v[iv].size(); jv++) { \
            cerr << v[iv][jv] << " ";               \
        }                                           \
        cerr << endl;                               \
    }
typedef long long ll;
// #define int ll

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
    return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template <class S, class T>
ostream &operator<<(ostream &os, pair<S, T> p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n) - 1; i >= 0; i--)
#define rrep1(i, n) for (int i = (int)(n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
void YES(bool t = true) {
    cout << (t ? "YES" : "NO") << endl;
}
void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; }
void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; }
void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; }
void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; }
void no(bool t = true) { cout << (t ? "no" : "yes") << endl; }
template <class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
T ceil_div(T a, T b) {
    return (a + b - 1) / b;
}
template <class T>
T safe_mul(T a, T b) {
    if (a == 0 || b == 0) return 0;
    if (numeric_limits<T>::max() / a < b) return numeric_limits<T>::max();
    return a * b;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
int popcount(ll t) { return __builtin_popcountll(t); }
vector<int> gen_perm(int n) {
    vector<int> ret(n);
    iota(all(ret), 0);
    return ret;
}
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {0, 0, -1, 1}, dy = {-1, 1, 0, 0};
vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1};
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(25);
        cerr << fixed << setprecision(25);
    }
} setup_io;
// constexpr ll MOD = 1000000007;
constexpr ll MOD = 998244353;
// #define mp make_pair

template <uint32_t mod>
struct LazyMontgomeryModInt {
    using mint = LazyMontgomeryModInt;
    using i32 = int32_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static constexpr u32 get_r() {
        u32 ret = mod;
        for (i32 i = 0; i < 4; ++i)
            ret *= 2 - mod * ret;
        return ret;
    }

    static constexpr u32 r = get_r();
    static constexpr u32 n2 = -u64(mod) % mod;
    static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
    static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
    static_assert(r * mod == 1, "this code has bugs.");

    u32 a;

    constexpr LazyMontgomeryModInt() : a(0) {}
    constexpr LazyMontgomeryModInt(const int64_t &b)
        : a(reduce(u64(b % mod + mod) * n2)){};

    static constexpr u32 reduce(const u64 &b) {
        return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
    }

    constexpr mint &operator+=(const mint &b) {
        if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    constexpr mint &operator-=(const mint &b) {
        if (i32(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    constexpr mint &operator*=(const mint &b) {
        a = reduce(u64(a) * b.a);
        return *this;
    }

    constexpr mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }

    constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
    constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
    constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
    constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
    constexpr bool operator==(const mint &b) const {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr bool operator!=(const mint &b) const {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr mint operator-() const { return mint() - mint(*this); }
    constexpr mint operator+() const { return mint(*this); }

    constexpr mint pow(u64 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    constexpr mint inverse() const {
        int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
        while (y > 0) {
            t = x / y;
            x -= t * y, u -= t * v;
            tmp = x, x = y, y = tmp;
            tmp = u, u = v, v = tmp;
        }
        return mint{u};
    }

    friend ostream &operator<<(ostream &os, const mint &b) {
        return os << b.get();
    }

    friend istream &operator>>(istream &is, mint &b) {
        int64_t t;
        is >> t;
        b = LazyMontgomeryModInt<mod>(t);
        return (is);
    }

    constexpr u32 get() const {
        u32 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static constexpr u32 get_mod() { return mod; }
};

template <typename mint>
struct NTT {
    static constexpr uint32_t get_pr() {
        uint32_t _mod = mint::get_mod();
        using u64 = uint64_t;
        u64 ds[32] = {};
        int idx = 0;
        u64 m = _mod - 1;
        for (u64 i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                ds[idx++] = i;
                while (m % i == 0)
                    m /= i;
            }
        }
        if (m != 1) ds[idx++] = m;

        uint32_t _pr = 2;
        while (1) {
            int flg = 1;
            for (int i = 0; i < idx; ++i) {
                u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
                while (b) {
                    if (b & 1) r = r * a % _mod;
                    a = a * a % _mod;
                    b >>= 1;
                }
                if (r == 1) {
                    flg = 0;
                    break;
                }
            }
            if (flg == 1) break;
            ++_pr;
        }
        return _pr;
    };

    static constexpr uint32_t mod = mint::get_mod();
    static constexpr uint32_t pr = get_pr();
    static constexpr int level = __builtin_ctzll(mod - 1);
    mint dw[level], dy[level];

    void setwy(int k) {
        mint w[level], y[level];
        w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
        y[k - 1] = w[k - 1].inverse();
        for (int i = k - 2; i > 0; --i)
            w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
        dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
        for (int i = 3; i < k; ++i) {
            dw[i] = dw[i - 1] * y[i - 2] * w[i];
            dy[i] = dy[i - 1] * w[i - 2] * y[i];
        }
    }

    NTT() { setwy(level); }

    void fft4(vector<mint> &a, int k) {
        if ((int)a.size() <= 1) return;
        if (k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        if (k & 1) {
            int v = 1 << (k - 1);
            for (int j = 0; j < v; ++j) {
                mint ajv = a[j + v];
                a[j + v] = a[j] - ajv;
                a[j] += ajv;
            }
        }
        int u = 1 << (2 + (k & 1));
        int v = 1 << (k - 2 - (k & 1));
        mint one = mint(1);
        mint imag = dw[1];
        while (v) {
            // jh = 0
            {
                int j0 = 0;
                int j1 = v;
                int j2 = j1 + v;
                int j3 = j2 + v;
                for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
                    mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
                }
            }
            // jh >= 1
            mint ww = one, xx = one * dw[2], wx = one;
            for (int jh = 4; jh < u;) {
                ww = xx * xx, wx = ww * xx;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for (; j0 < je; ++j0, ++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
                         t3 = a[j2 + v] * wx;
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
                }
                xx *= dw[__builtin_ctzll((jh += 4))];
            }
            u <<= 2;
            v >>= 2;
        }
    }

    void ifft4(vector<mint> &a, int k) {
        if ((int)a.size() <= 1) return;
        if (k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        int u = 1 << (k - 2);
        int v = 1;
        mint one = mint(1);
        mint imag = dy[1];
        while (u) {
            // jh = 0
            {
                int j0 = 0;
                int j1 = v;
                int j2 = v + v;
                int j3 = j2 + v;
                for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
                    mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
                    a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
                    a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
                }
            }
            // jh >= 1
            mint ww = one, xx = one * dy[2], yy = one;
            u <<= 2;
            for (int jh = 4; jh < u;) {
                ww = xx * xx, yy = xx * imag;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for (; j0 < je; ++j0, ++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
                    a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
                    a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
                }
                xx *= dy[__builtin_ctzll(jh += 4)];
            }
            u >>= 4;
            v <<= 2;
        }
        if (k & 1) {
            u = 1 << (k - 1);
            for (int j = 0; j < u; ++j) {
                mint ajv = a[j] - a[j + u];
                a[j] += a[j + u];
                a[j + u] = ajv;
            }
        }
    }

    void ntt(vector<mint> &a) {
        if ((int)a.size() <= 1) return;
        fft4(a, __builtin_ctz(a.size()));
    }

    void intt(vector<mint> &a) {
        if ((int)a.size() <= 1) return;
        ifft4(a, __builtin_ctz(a.size()));
        mint iv = mint(a.size()).inverse();
        for (auto &x : a)
            x *= iv;
    }

    vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
        int l = a.size() + b.size() - 1;
        if (min<int>(a.size(), b.size()) <= 40) {
            vector<mint> s(l);
            for (int i = 0; i < (int)a.size(); ++i)
                for (int j = 0; j < (int)b.size(); ++j)
                    s[i + j] += a[i] * b[j];
            return s;
        }
        int k = 2, M = 4;
        while (M < l)
            M <<= 1, ++k;
        setwy(k);
        vector<mint> s(M);
        for (int i = 0; i < (int)a.size(); ++i)
            s[i] = a[i];
        fft4(s, k);
        if (a.size() == b.size() && a == b) {
            for (int i = 0; i < M; ++i)
                s[i] *= s[i];
        } else {
            vector<mint> t(M);
            for (int i = 0; i < (int)b.size(); ++i)
                t[i] = b[i];
            fft4(t, k);
            for (int i = 0; i < M; ++i)
                s[i] *= t[i];
        }
        ifft4(s, k);
        s.resize(l);
        mint invm = mint(M).inverse();
        for (int i = 0; i < l; ++i)
            s[i] *= invm;
        return s;
    }

    void ntt_doubling(vector<mint> &a) {
        int M = (int)a.size();
        auto b = a;
        intt(b);
        mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
        for (int i = 0; i < M; i++)
            b[i] *= r, r *= zeta;
        ntt(b);
        copy(begin(b), end(b), back_inserter(a));
    }
};

template <typename mint>
struct FormalPowerSeries : vector<mint> {
    using vector<mint>::vector;
    using FPS = FormalPowerSeries;

    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];
        return *this;
    }

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

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

    FPS &operator*=(const mint &v) {
        for (int k = 0; k < (int)this->size(); k++)
            (*this)[k] *= v;
        return *this;
    }

    FPS &operator/=(const FPS &r) {
        if (this->size() < r.size()) {
            this->clear();
            return *this;
        }
        int n = this->size() - r.size() + 1;
        if ((int)r.size() <= 64) {
            FPS f(*this), g(r);
            g.shrink();
            mint coeff = g.back().inverse();
            for (auto &x : g)
                x *= coeff;
            int deg = (int)f.size() - (int)g.size() + 1;
            int gs = g.size();
            FPS quo(deg);
            for (int i = deg - 1; i >= 0; i--) {
                quo[i] = f[i + gs - 1];
                for (int j = 0; j < gs; j++)
                    f[i + j] -= quo[i] * g[j];
            }
            *this = quo * coeff;
            this->resize(n, mint(0));
            return *this;
        }
        return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
    }

    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 mint &v) const { return FPS(*this) += v; }
    FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
    FPS operator-(const mint &v) const { return FPS(*this) -= v; }
    FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
    FPS operator*(const mint &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->size());
        for (int i = 0; i < (int)this->size(); i++)
            ret[i] = -(*this)[i];
        return ret;
    }

    void shrink() {
        while (this->size() && this->back() == mint(0))
            this->pop_back();
    }

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

    FPS dot(FPS r) const {
        FPS ret(min(this->size(), r.size()));
        for (int i = 0; i < (int)ret.size(); i++)
            ret[i] = (*this)[i] * r[i];
        return ret;
    }

    // 前 sz 項を取ってくる。sz に足りない項は 0 埋めする
    FPS pre(int sz) const {
        FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));
        if ((int)ret.size() < sz) ret.resize(sz);
        return ret;
    }

    FPS operator>>(int sz) const {
        if ((int)this->size() <= sz) return {};
        FPS ret(*this);
        ret.erase(ret.begin(), ret.begin() + sz);
        return ret;
    }

    FPS operator<<(int sz) const {
        FPS ret(*this);
        ret.insert(ret.begin(), sz, mint(0));
        return ret;
    }

    FPS diff() const {
        const int n = (int)this->size();
        FPS ret(max(0, n - 1));
        mint one(1), coeff(1);
        for (int i = 1; i < n; i++) {
            ret[i - 1] = (*this)[i] * coeff;
            coeff += one;
        }
        return ret;
    }

    FPS integral() const {
        const int n = (int)this->size();
        FPS ret(n + 1);
        ret[0] = mint(0);
        if (n > 0) ret[1] = mint(1);
        auto mod = mint::get_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;
    }

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

    FPS log(int deg = -1) const {
        assert(!(*this).empty() && (*this)[0] == mint(1));
        if (deg == -1) deg = (int)this->size();
        return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
    }

    FPS pow(int64_t k, int deg = -1) const {
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        if (k == 0) {
            FPS ret(deg);
            if (deg) ret[0] = 1;
            return ret;
        }
        for (int i = 0; i < n; i++) {
            if ((*this)[i] != mint(0)) {
                mint rev = mint(1) / (*this)[i];
                FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
                ret *= (*this)[i].pow(k);
                ret = (ret << (i * k)).pre(deg);
                if ((int)ret.size() < deg) ret.resize(deg, mint(0));
                return ret;
            }
            if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));
        }
        return FPS(deg, mint(0));
    }

    static void *ntt_ptr;
    static void set_fft();
    FPS &operator*=(const FPS &r);
    void ntt();
    void intt();
    void ntt_doubling();
    static int ntt_pr();
    FPS inv(int deg = -1) const;
    FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;

template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
    if (!ntt_ptr) ntt_ptr = new NTT<mint>;
}

template <typename mint>
FormalPowerSeries<mint> &FormalPowerSeries<mint>::operator*=(
    const FormalPowerSeries<mint> &r) {
    if (this->empty() || r.empty()) {
        this->clear();
        return *this;
    }
    set_fft();
    auto ret = static_cast<NTT<mint> *>(ntt_ptr)->multiply(*this, r);
    return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}

template <typename mint>
void FormalPowerSeries<mint>::ntt() {
    set_fft();
    static_cast<NTT<mint> *>(ntt_ptr)->ntt(*this);
}

template <typename mint>
void FormalPowerSeries<mint>::intt() {
    set_fft();
    static_cast<NTT<mint> *>(ntt_ptr)->intt(*this);
}

template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
    set_fft();
    static_cast<NTT<mint> *>(ntt_ptr)->ntt_doubling(*this);
}

template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
    set_fft();
    return static_cast<NTT<mint> *>(ntt_ptr)->pr;
}

template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
    assert((*this)[0] != mint(0));
    if (deg == -1) deg = (int)this->size();
    FormalPowerSeries<mint> res(deg);
    res[0] = {mint(1) / (*this)[0]};
    for (int d = 1; d < deg; d <<= 1) {
        FormalPowerSeries<mint> f(2 * d), g(2 * d);
        for (int j = 0; j < min((int)this->size(), 2 * d); j++)
            f[j] = (*this)[j];
        for (int j = 0; j < d; j++)
            g[j] = res[j];
        f.ntt();
        g.ntt();
        for (int j = 0; j < 2 * d; j++)
            f[j] *= g[j];
        f.intt();
        for (int j = 0; j < d; j++)
            f[j] = 0;
        f.ntt();
        for (int j = 0; j < 2 * d; j++)
            f[j] *= g[j];
        f.intt();
        for (int j = d; j < min(2 * d, deg); j++)
            res[j] = -f[j];
    }
    return res.pre(deg);
}

template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
    using fps = FormalPowerSeries<mint>;
    assert((*this).size() == 0 || (*this)[0] == mint(0));
    if (deg == -1) deg = this->size();

    fps inv;
    inv.reserve(deg + 1);
    inv.push_back(mint(0));
    inv.push_back(mint(1));

    auto inplace_integral = [&](fps &F) -> void {
        const int n = (int)F.size();
        auto mod = mint::get_mod();
        while ((int)inv.size() <= n) {
            int i = inv.size();
            inv.push_back((-inv[mod % i]) * (mod / i));
        }
        F.insert(begin(F), mint(0));
        for (int i = 1; i <= n; i++)
            F[i] *= inv[i];
    };

    auto inplace_diff = [](fps &F) -> void {
        if (F.empty()) return;
        F.erase(begin(F));
        mint coeff = 1, one = 1;
        for (int i = 0; i < (int)F.size(); i++) {
            F[i] *= coeff;
            coeff += one;
        }
    };

    fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
    for (int m = 2; m < deg; m *= 2) {
        auto y = b;
        y.resize(2 * m);
        y.ntt();
        z1 = z2;
        fps z(m);
        for (int i = 0; i < m; ++i)
            z[i] = y[i] * z1[i];
        z.intt();
        fill(begin(z), begin(z) + m / 2, mint(0));
        z.ntt();
        for (int i = 0; i < m; ++i)
            z[i] *= -z1[i];
        z.intt();
        c.insert(end(c), begin(z) + m / 2, end(z));
        z2 = c;
        z2.resize(2 * m);
        z2.ntt();
        fps x(begin(*this), begin(*this) + min<int>(this->size(), m));
        x.resize(m);
        inplace_diff(x);
        x.push_back(mint(0));
        x.ntt();
        for (int i = 0; i < m; ++i)
            x[i] *= y[i];
        x.intt();
        x -= b.diff();
        x.resize(2 * m);
        for (int i = 0; i < m - 1; ++i)
            x[m + i] = x[i], x[i] = mint(0);
        x.ntt();
        for (int i = 0; i < 2 * m; ++i)
            x[i] *= z2[i];
        x.intt();
        x.pop_back();
        inplace_integral(x);
        for (int i = m; i < min<int>(this->size(), 2 * m); ++i)
            x[i] += (*this)[i];
        fill(begin(x), begin(x) + m, mint(0));
        x.ntt();
        for (int i = 0; i < 2 * m; ++i)
            x[i] *= y[i];
        x.intt();
        b.insert(end(b), begin(x) + m, end(x));
    }
    return fps{begin(b), begin(b) + deg};
}

template <typename mint>
mint LinearRecurrence(long long k, FormalPowerSeries<mint> Q,
                      FormalPowerSeries<mint> P) {
    Q.shrink();
    mint ret = 0;
    if (P.size() >= Q.size()) {
        auto R = P / Q;
        P -= R * Q;
        P.shrink();
        if (k < (int)R.size()) ret += R[k];
    }
    if ((int)P.size() == 0) return ret;

    FormalPowerSeries<mint>::set_fft();
    if (FormalPowerSeries<mint>::ntt_ptr == nullptr) {
        P.resize((int)Q.size() - 1);
        while (k) {
            auto Q2 = Q;
            for (int i = 1; i < (int)Q2.size(); i += 2)
                Q2[i] = -Q2[i];
            auto S = P * Q2;
            auto T = Q * Q2;
            if (k & 1) {
                for (int i = 1; i < (int)S.size(); i += 2)
                    P[i >> 1] = S[i];
                for (int i = 0; i < (int)T.size(); i += 2)
                    Q[i >> 1] = T[i];
            } else {
                for (int i = 0; i < (int)S.size(); i += 2)
                    P[i >> 1] = S[i];
                for (int i = 0; i < (int)T.size(); i += 2)
                    Q[i >> 1] = T[i];
            }
            k >>= 1;
        }
        return ret + P[0];
    } else {
        int N = 1;
        while (N < (int)Q.size())
            N <<= 1;

        P.resize(2 * N);
        Q.resize(2 * N);
        P.ntt();
        Q.ntt();
        vector<mint> S(2 * N), T(2 * N);

        vector<int> btr(N);
        for (int i = 0, logn = __builtin_ctz(N); i < (1 << logn); i++) {
            btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (logn - 1));
        }
        mint dw = mint(FormalPowerSeries<mint>::ntt_pr())
                      .inverse()
                      .pow((mint::get_mod() - 1) / (2 * N));

        while (k) {
            mint inv2 = mint(2).inverse();

            // even degree of Q(x)Q(-x)
            T.resize(N);
            for (int i = 0; i < N; i++)
                T[i] = Q[(i << 1) | 0] * Q[(i << 1) | 1];

            S.resize(N);
            if (k & 1) {
                // odd degree of P(x)Q(-x)
                for (auto &i : btr) {
                    S[i] = (P[(i << 1) | 0] * Q[(i << 1) | 1] -
                            P[(i << 1) | 1] * Q[(i << 1) | 0]) *
                           inv2;
                    inv2 *= dw;
                }
            } else {
                // even degree of P(x)Q(-x)
                for (int i = 0; i < N; i++) {
                    S[i] = (P[(i << 1) | 0] * Q[(i << 1) | 1] +
                            P[(i << 1) | 1] * Q[(i << 1) | 0]) *
                           inv2;
                }
            }
            swap(P, S);
            swap(Q, T);
            k >>= 1;
            if (k < N) break;
            P.ntt_doubling();
            Q.ntt_doubling();
        }
        P.intt();
        Q.intt();
        return ret + (P * (Q.inv()))[k];
    }
}

template <typename mint>
mint kitamasa(long long N, FormalPowerSeries<mint> Q,
              FormalPowerSeries<mint> a) {
    assert(!Q.empty() && Q[0] != 0);
    if (N < (int)a.size()) return a[N];
    assert((int)a.size() >= int(Q.size()) - 1);
    auto P = a.pre((int)Q.size() - 1) * Q;
    P.resize(Q.size() - 1);
    return LinearRecurrence<mint>(N, Q, P);
}

template <typename mint>
vector<mint> BerlekampMassey(const vector<mint> &s) {
    const int N = (int)s.size();
    vector<mint> b, c;
    b.reserve(N + 1);
    c.reserve(N + 1);
    b.push_back(mint(1));
    c.push_back(mint(1));
    mint y = mint(1);
    for (int ed = 1; ed <= N; ed++) {
        int l = int(c.size()), m = int(b.size());
        mint x = 0;
        for (int i = 0; i < l; i++)
            x += c[i] * s[ed - l + i];
        b.emplace_back(mint(0));
        m++;
        if (x == mint(0)) continue;
        mint freq = x / y;
        if (l < m) {
            auto tmp = c;
            c.insert(begin(c), m - l, mint(0));
            for (int i = 0; i < m; i++)
                c[m - 1 - i] -= freq * b[m - 1 - i];
            b = tmp;
            y = x;
        } else {
            for (int i = 0; i < m; i++)
                c[l - 1 - i] -= freq * b[m - 1 - i];
        }
    }
    reverse(begin(c), end(c));
    return c;
}

template <typename mint>
mint nth_term(long long n, const vector<mint> &s) {
    // https://nyaannyaan.github.io/library/fps/nth-term.hpp.html
    // verify: https://atcoder.jp/contests/npcapc_2024/submissions/55211058
    // 線形漸化式の最初の数項が与えられた時に n 番目の項を求める。具体的な漸化式は与える必要がない
    // k-項間線形漸化式の場合 2k 項以上の数列が必要？
    // Berlekamp-Massey で O(k^2) で具体的な線形漸化式を与えることができる
    // その後、Bostan-Mori で O(k log k log n) で n 番目の項を求めることができる

    using fps = FormalPowerSeries<mint>;
    auto bm = BerlekampMassey<mint>(s);
    return kitamasa(n, fps{begin(bm), end(bm)}, fps{begin(s), end(s)});
}

using mint = LazyMontgomeryModInt<998244353>;

typedef vector<mint> vec;
typedef vector<vec> mat;

mat mul(const mat &A, const mat &B) {
    mat C(A.size(), vec(B[0].size()));
    for (int i = 0; i < A.size(); i++) {
        for (int k = 0; k < B.size(); k++) {
            for (int j = 0; j < B[0].size(); j++) {
                C[i][j] = C[i][j] + A[i][k] * B[k][j];
            }
        }
    }
    return C;
}

vec mul(const mat &A, const vec &B) {
    vec C(A.size());
    for (int i = 0; i < A.size(); i++) {
        for (int j = 0; j < B.size(); j++) {
            C[i] += A[i][j] * B[j];
        }
    }
    return C;
}

mat pow(mat A, ll n) {
    mat B(A.size(), vec(A.size()));
    for (int i = 0; i < A.size(); i++) {
        B[i][i] = 1;
    }
    while (n > 0) {
        if (n & 1) B = mul(B, A);
        A = mul(A, A);
        n >>= 1;
    }
    return B;
}

mat A = mat(6, vec(6));

mint calc(ll x) {
    // x 以上の移動の数
    mint ans = 0;
    for (ll y = x - 6; y < x; y++) {
        if (y < 0) continue;

        vec start(6);
        start[5] = 1;
        mat An = pow(A, y);
        vec res = mul(An, start);

        mint base = res[5];
        rep1(add, 6) {
            if (y + add >= x) {
                ans += base;
            }
        }
    }
    return ans;
}

void small(ll n, ll m, ll q, vl c) {
    mint zen = calc(n * m);
    DEBUG(zen);

    vector<mint> ans(n);

    for (int out = 1; out < n; out++) {
        vector<mint> est(110);
        for (int mm = 1; mm <= 110; mm++) {
            int N = n * mm;
            vector<mint> dp(N + 10);
            dp[0] = 1;
            rep(i, N) {
                rep1(j, 6) {
                    int ni = i + j;
                    if (ni % n == out && ni < N) {
                        continue;
                    }
                    dp[ni] += dp[i];
                }
            }

            for (int i = N; i < N + 10; i++) {
                est[mm - 1] += dp[i];
            }
        }

        ans[out] = nth_term(m - 1, est);
    }

    rep(i, q) {
        cout << zen - ans[c[i]] << endl;
    }
}

signed main() {
    ll n, m, q;
    cin >> n >> m >> q;
    vl c(q);
    rep(i, q) {
        cin >> c[i];
    }

    rep(i, 5) {
        A[i][i + 1] = 1;
    }
    rep(i, 6) {
        A[5][i] = 1;
    }

    mint zen = calc(n * m);

    if (n <= 20) {
        small(n, m, q, c);
        return 0;
    }
    assert(false);
}