#include <bits/stdc++.h>
#include <immintrin.h>
/**
 * ライブラリはNyaanさんのライブラリを拝借しています 
 * https://nyaannyaan.github.io/library/ntt/multivariate-multiplication.hpp
 */
#pragma region Header
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using f64 = double;
using f80 = long double;
using f128 = __float128;
constexpr i32 operator"" _i32(u64 v)
{
    return v;
}
constexpr i32 operator"" _u32(u64 v)
{
    return v;
}
constexpr i64 operator"" _i64(u64 v)
{
    return v;
}
constexpr u64 operator"" _u64(u64 v)
{
    return v;
}
constexpr f64 operator"" _f64(f80 v)
{
    return v;
}
constexpr f80 operator"" _f80(f80 v)
{
    return v;
}
using Istream = std::istream;
using Ostream = std::ostream;
using Str = std::string;
template<typename T>
using Lt = std::less<T>;
template<typename T>
using Gt = std::greater<T>;
template<typename T>
using IList = std::initializer_list<T>;
template<int n>
using BSet = std::bitset<n>;
template<typename T1, typename T2>
using Pair = std::pair<T1, T2>;
template<typename... Ts>
using Tup = std::tuple<Ts...>;
template<typename T, int N>
using Arr = std::array<T, N>;
template<typename... Ts>
using Deq = std::deque<Ts...>;
template<typename... Ts>
using Set = std::set<Ts...>;
template<typename... Ts>
using MSet = std::multiset<Ts...>;
template<typename... Ts>
using USet = std::unordered_set<Ts...>;
template<typename... Ts>
using UMSet = std::unordered_multiset<Ts...>;
template<typename... Ts>
using Map = std::map<Ts...>;
template<typename... Ts>
using MMap = std::multimap<Ts...>;
template<typename... Ts>
using UMap = std::unordered_map<Ts...>;
template<typename... Ts>
using UMMap = std::unordered_multimap<Ts...>;
template<typename... Ts>
using Vec = std::vector<Ts...>;
template<typename... Ts>
using Stack = std::stack<Ts...>;
template<typename... Ts>
using Queue = std::queue<Ts...>;
template<typename T>
using MaxHeap = std::priority_queue<T>;
template<typename T>
using MinHeap = std::priority_queue<T, Vec<T>, Gt<T>>;
using NSec = std::chrono::nanoseconds;
using USec = std::chrono::microseconds;
using MSec = std::chrono::milliseconds;
using Sec = std::chrono::seconds;
template<typename T>
constexpr T LIMMIN = std::numeric_limits<T>::min();
template<typename T>
constexpr T LIMMAX = std::numeric_limits<T>::max();
template<typename T>
constexpr T INF = (LIMMAX<T> - 1) / 2;
template<typename T>
constexpr T PI = T{3.141592653589793238462643383279502884};
template<typename T = u64>
constexpr T TEN(const int n)
{
    return n == 0 ? T{1} : TEN<T>(n - 1) * T{10};
}
Ostream& operator<<(Ostream& os, i128 v)
{
    bool minus = false;
    if (v < 0) { minus = true, v = -v; }
    Str ans;
    if (v == 0) { ans = "0"; }
    while (v) {
        ans.push_back('0' + v % 10), v /= 10;
    }
    std::reverse(ans.begin(), ans.end());
    return os << (minus ? "-" : "") << ans;
}
Ostream& operator<<(Ostream& os, u128 v)
{
    Str ans;
    if (v == 0) { ans = "0"; }
    while (v) {
        ans.push_back('0' + v % 10), v /= 10;
    }
    std::reverse(ans.begin(), ans.end());
    return os << ans;
}
template<typename T>
bool chmin(T& a, const T& b)
{
    if (a > b) {
        a = b;
        return true;
    } else {
        return false;
    }
}
template<typename T>
bool chmax(T& a, const T& b)
{
    if (a < b) {
        a = b;
        return true;
    } else {
        return false;
    }
}
template<typename T>
constexpr T floorDiv(T x, T y)
{
    if (y < T{}) { x = -x, y = -y; }
    return x >= T{} ? x / y : (x - y + 1) / y;
}
template<typename T>
constexpr T ceilDiv(T x, T y)
{
    if (y < T{}) { x = -x, y = -y; }
    return x >= T{} ? (x + y - 1) / y : x / y;
}
template<typename T, typename I>
constexpr T modPower(T v, I n, T mod)
{
    T ans = 1 % mod;
    for (; n > 0; n >>= 1, (v *= v) %= mod) {
        if (n % 2 == 1) { (ans *= v) %= mod; }
    }
    return ans;
}
template<typename T, typename I>
constexpr T power(T v, I n)
{
    T ans = 1;
    for (; n > 0; n >>= 1, v *= v) {
        if (n % 2 == 1) { ans *= v; }
    }
    return ans;
}
template<typename T, typename I>
constexpr T power(T v, I n, const T& e)
{
    T ans = e;
    for (; n > 0; n >>= 1, v *= v) {
        if (n % 2 == 1) { ans *= v; }
    }
    return ans;
}
template<typename T>
Vec<T> operator+=(Vec<T>& vs1, const Vec<T>& vs2)
{
    vs1.insert(vs1.end(), vs2.begin(), vs2.end());
    return vs1;
}
template<typename T>
Vec<T> operator+(const Vec<T>& vs1, const Vec<T>& vs2)
{
    auto vs = vs1;
    vs += vs2;
    return vs;
}
template<typename Vs, typename V>
void fillAll(Vs& arr, const V& v)
{
    if constexpr (std::is_convertible<V, Vs>::value) {
        arr = v;
    } else {
        for (auto& subarr : arr) {
            fillAll(subarr, v);
        }
    }
}
template<typename Vs>
void sortAll(Vs& vs)
{
    std::sort(std::begin(vs), std::end(vs));
}
template<typename Vs, typename C>
void sortAll(Vs& vs, C comp)
{
    std::sort(std::begin(vs), std::end(vs), comp);
}
template<typename Vs>
void reverseAll(Vs& vs)
{
    std::reverse(std::begin(vs), std::end(vs));
}
template<typename V, typename Vs>
V sumAll(const Vs& vs)
{
    if constexpr (std::is_convertible<Vs, V>::value) {
        return static_cast<V>(vs);
    } else {
        V ans = 0;
        for (const auto& v : vs) {
            ans += sumAll<V>(v);
        }
        return ans;
    }
}
template<typename Vs>
int minInd(const Vs& vs)
{
    return std::min_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs>
int maxInd(const Vs& vs)
{
    return std::max_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs, typename V>
int lbInd(const Vs& vs, const V& v)
{
    return std::lower_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename Vs, typename V>
int ubInd(const Vs& vs, const V& v)
{
    return std::upper_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename T, typename F>
Vec<T> genVec(int n, F gen)
{
    Vec<T> ans;
    std::generate_n(std::back_insert_iterator(ans), n, gen);
    return ans;
}
Vec<int> iotaVec(int n, int offset = 0)
{
    Vec<int> ans(n);
    std::iota(ans.begin(), ans.end(), offset);
    return ans;
}
constexpr int popcount(const u64 v)
{
    return v ? __builtin_popcountll(v) : 0;
}
constexpr int log2p1(const u64 v)
{
    return v ? 64 - __builtin_clzll(v) : 0;
}
constexpr int lsbp1(const u64 v)
{
    return __builtin_ffsll(v);
}
constexpr int clog(const u64 v)
{
    return v ? log2p1(v - 1) : 0;
}
constexpr u64 ceil2(const u64 v)
{
    const int l = clog(v);
    return (l == 64) ? 0_u64 : (1_u64 << l);
}
constexpr u64 floor2(const u64 v)
{
    return v ? (1_u64 << (log2p1(v) - 1)) : 0_u64;
}
constexpr bool ispow2(const u64 v)
{
    return (v > 0) and ((v & (v - 1)) == 0);
}
constexpr bool btest(const u64 mask, const int ind)
{
    return (mask >> ind) & 1_u64;
}
template<typename F>
struct Fix : F
{
    Fix(F&& f) : F{std::forward<F>(f)} {}
    template<typename... Args>
    auto operator()(Args&&... args) const
    {
        return F::operator()(*this, std::forward<Args>(args)...);
    }
};
class irange
{
private:
    struct itr
    {
        itr(i64 start = 0, i64 step = 1) : m_cnt{start}, m_step{step} {}
        bool operator!=(const itr& it) const
        {
            return m_cnt != it.m_cnt;
        }
        int operator*()
        {
            return m_cnt;
        }
        itr& operator++()
        {
            m_cnt += m_step;
            return *this;
        }
        i64 m_cnt, m_step;
    };
    i64 m_start, m_end, m_step;
public:
    irange(i64 start, i64 end, i64 step = 1)
    {
        assert(step != 0);
        const i64 d = std::abs(step);
        const i64 l = (step > 0 ? start : end);
        const i64 r = (step > 0 ? end : start);
        int n = (r - l) / d + ((r - l) % d ? 1 : 0);
        if (l >= r) { n = 0; }
        m_start = start;
        m_end = start + step * n;
        m_step = step;
    }
    itr begin() const
    {
        return itr{m_start, m_step};
    }
    itr end() const
    {
        return itr{m_end, m_step};
    }
};
irange rep(int end)
{
    return irange(0, end, 1);
}
irange per(int rend)
{
    return irange(rend - 1, -1, -1);
}
#pragma COMMENT("[REFS] Xoshiro: https://prng.di.unimi.it")
namespace xoshiro_impl {
u64 x;
u64 next()
{
    uint64_t z = (x += 0x9e3779b97f4a7c15);
    z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
    z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
    return z ^ (z >> 31);
}
} // namespace xoshiro_impl
class Xoshiro32
{
public:
    using result_type = u32;
    using T = result_type;
    Xoshiro32(T seed = 0)
    {
        xoshiro_impl::x = seed;
        s[0] = xoshiro_impl::next();
        s[1] = xoshiro_impl::next();
        s[2] = xoshiro_impl::next();
        s[3] = xoshiro_impl::next();
    }
    static constexpr T min()
    {
        return LIMMIN<T>;
    }
    static constexpr T max()
    {
        return LIMMAX<T>;
    }
    T operator()()
    {
        return next();
    }
private:
    static constexpr T rotl(const T x, int k)
    {
        return (x << k) | (x >> (32 - k));
    }
    T next()
    {
        const T ans = rotl(s[1] * 5, 7) * 9;
        const T t = s[1] << 9;
        s[2] ^= s[0];
        s[3] ^= s[1];
        s[1] ^= s[2];
        s[0] ^= s[3];
        s[2] ^= t;
        s[3] = rotl(s[3], 11);
        return ans;
    }
    T s[4];
};
class Xoshiro64
{
public:
    using result_type = u64;
    using T = result_type;
    Xoshiro64(T seed = 0)
    {
        xoshiro_impl::x = seed;
        s[0] = xoshiro_impl::next();
        s[1] = xoshiro_impl::next();
        s[2] = xoshiro_impl::next();
        s[3] = xoshiro_impl::next();
    }
    static constexpr T min()
    {
        return LIMMIN<T>;
    }
    static constexpr T max()
    {
        return LIMMAX<T>;
    }
    T operator()()
    {
        return next();
    }
private:
    static constexpr T rotl(const T x, int k)
    {
        return (x << k) | (x >> (64 - k));
    }
    T next()
    {
        const T ans = rotl(s[1] * 5, 7) * 9;
        const T t = s[1] << 17;
        s[2] ^= s[0];
        s[3] ^= s[1];
        s[1] ^= s[2];
        s[0] ^= s[3];
        s[2] ^= t;
        s[3] = rotl(s[3], 45);
        return ans;
    }
    T s[4];
};
template<typename Rng>
class RNG
{
public:
    using result_type = typename Rng::result_type;
    using T = result_type;
    static constexpr T min()
    {
        return Rng::min();
    }
    static constexpr T max()
    {
        return Rng::max();
    }
    RNG() : RNG(std::random_device{}()) {}
    RNG(T seed) : m_rng(seed) {}
    T operator()()
    {
        return m_rng();
    }
    template<typename T>
    T val(T min, T max)
    {
        return std::uniform_int_distribution<T>(min, max)(m_rng);
    }
    template<typename T>
    Pair<T, T> pair(T min, T max)
    {
        return std::minmax({val<T>(min, max), val<T>(min, max)});
    }
    template<typename T>
    Vec<T> vec(int n, T min, T max)
    {
        return genVec<T>(n, [&]() { return val<T>(min, max); });
    }
    template<typename T>
    Vec<Vec<T>> vvec(int n, int m, T min, T max)
    {
        return genVec<Vec<T>>(n, [&]() { return vec(m, min, max); });
    }
private:
    Rng m_rng;
};
RNG<std::mt19937> rng;
RNG<std::mt19937_64> rng64;
RNG<Xoshiro32> rng_xo;
RNG<Xoshiro64> rng_xo64;
class Scanner
{
public:
    Scanner(Istream& is = std::cin) : m_is{is}
    {
        m_is.tie(nullptr)->sync_with_stdio(false);
    }
    template<typename T>
    T val()
    {
        T v;
        return m_is >> v, v;
    }
    template<typename T>
    T val(T offset)
    {
        return val<T>() - offset;
    }
    template<typename T>
    Vec<T> vec(int n)
    {
        return genVec<T>(n, [&]() { return val<T>(); });
    }
    template<typename T>
    Vec<T> vec(int n, T offset)
    {
        return genVec<T>(n, [&]() { return val<T>(offset); });
    }
    template<typename T>
    Vec<Vec<T>> vvec(int n, int m)
    {
        return genVec<Vec<T>>(n, [&]() { return vec<T>(m); });
    }
    template<typename T>
    Vec<Vec<T>> vvec(int n, int m, const T offset)
    {
        return genVec<Vec<T>>(n, [&]() { return vec<T>(m, offset); });
    }
    template<typename... Args>
    auto tup()
    {
        return Tup<Args...>{val<Args>()...};
    }
    template<typename... Args>
    auto tup(const Args&... offsets)
    {
        return Tup<Args...>{val<Args>(offsets)...};
    }
private:
    Istream& m_is;
};
Scanner in;
class Printer
{
public:
    Printer(Ostream& os = std::cout) : m_os{os}
    {
        m_os << std::fixed << std::setprecision(15);
    }
    template<typename... Args>
    int operator()(const Args&... args)
    {
        dump(args...);
        return 0;
    }
    template<typename... Args>
    int ln(const Args&... args)
    {
        dump(args...), m_os << '\n';
        return 0;
    }
    template<typename... Args>
    int el(const Args&... args)
    {
        dump(args...), m_os << std::endl;
        return 0;
    }
private:
    template<typename T>
    void dump(const T& v)
    {
        m_os << v;
    }
    template<typename T>
    void dump(const Vec<T>& vs)
    {
        for (const int i : rep(vs.size())) {
            m_os << (i ? " " : ""), dump(vs[i]);
        }
    }
    template<typename T>
    void dump(const Vec<Vec<T>>& vss)
    {
        for (const int i : rep(vss.size())) {
            m_os << (i ? "\n" : ""), dump(vss[i]);
        }
    }
    template<typename T, typename... Ts>
    int dump(const T& v, const Ts&... args)
    {
        dump(v), m_os << ' ', dump(args...);
        return 0;
    }
    Ostream& m_os;
};
Printer out;
#pragma endregion
__attribute__((target("sse4.2"))) inline __m128i
    my128_mullo_epu32(const __m128i& a, const __m128i& b)
{
    return _mm_mullo_epi32(a, b);
}
__attribute__((target("sse4.2"))) inline __m128i
    my128_mulhi_epu32(const __m128i& a, const __m128i& b)
{
    __m128i a13 = _mm_shuffle_epi32(a, 0xF5);
    __m128i b13 = _mm_shuffle_epi32(b, 0xF5);
    __m128i prod02 = _mm_mul_epu32(a, b);
    __m128i prod13 = _mm_mul_epu32(a13, b13);
    __m128i prod = _mm_unpackhi_epi64(_mm_unpacklo_epi32(prod02, prod13),
                                      _mm_unpackhi_epi32(prod02, prod13));
    return prod;
}
__attribute__((target("sse4.2"))) inline __m128i
    montgomery_mul_128(const __m128i& a,
                       const __m128i& b,
                       const __m128i& r,
                       const __m128i& m1)
{
    return _mm_sub_epi32(
        _mm_add_epi32(my128_mulhi_epu32(a, b), m1),
        my128_mulhi_epu32(my128_mullo_epu32(my128_mullo_epu32(a, b), r), m1));
}
__attribute__((target("sse4.2"))) inline __m128i
    montgomery_add_128(const __m128i& a,
                       const __m128i& b,
                       const __m128i& m2,
                       const __m128i& m0)
{
    __m128i ret = _mm_sub_epi32(_mm_add_epi32(a, b), m2);
    return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("sse4.2"))) inline __m128i
    montgomery_sub_128(const __m128i& a,
                       const __m128i& b,
                       const __m128i& m2,
                       const __m128i& m0)
{
    __m128i ret = _mm_sub_epi32(a, b);
    return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("avx2"))) inline __m256i
    my256_mullo_epu32(const __m256i& a, const __m256i& b)
{
    return _mm256_mullo_epi32(a, b);
}
__attribute__((target("avx2"))) inline __m256i
    my256_mulhi_epu32(const __m256i& a, const __m256i& b)
{
    __m256i a13 = _mm256_shuffle_epi32(a, 0xF5);
    __m256i b13 = _mm256_shuffle_epi32(b, 0xF5);
    __m256i prod02 = _mm256_mul_epu32(a, b);
    __m256i prod13 = _mm256_mul_epu32(a13, b13);
    __m256i prod = _mm256_unpackhi_epi64(_mm256_unpacklo_epi32(prod02, prod13),
                                         _mm256_unpackhi_epi32(prod02, prod13));
    return prod;
}
__attribute__((target("avx2"))) inline __m256i
    montgomery_mul_256(const __m256i& a,
                       const __m256i& b,
                       const __m256i& r,
                       const __m256i& m1)
{
    return _mm256_sub_epi32(
        _mm256_add_epi32(my256_mulhi_epu32(a, b), m1),
        my256_mulhi_epu32(my256_mullo_epu32(my256_mullo_epu32(a, b), r), m1));
}
__attribute__((target("avx2"))) inline __m256i
    montgomery_add_256(const __m256i& a,
                       const __m256i& b,
                       const __m256i& m2,
                       const __m256i& m0)
{
    __m256i ret = _mm256_sub_epi32(_mm256_add_epi32(a, b), m2);
    return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
                            ret);
}
__attribute__((target("avx2"))) inline __m256i
    montgomery_sub_256(const __m256i& a,
                       const __m256i& b,
                       const __m256i& m2,
                       const __m256i& m0)
{
    __m256i ret = _mm256_sub_epi32(a, b);
    return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
                            ret);
}
namespace ntt_inner {
using u64 = uint64_t;
constexpr uint32_t get_pr(uint32_t mod)
{
    if (mod == 2) return 1;
    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;
}
constexpr int SZ_FFT_BUF = 1 << 23;
uint32_t _buf1[SZ_FFT_BUF] __attribute__((aligned(64)));
uint32_t _buf2[SZ_FFT_BUF] __attribute__((aligned(64)));
} // namespace ntt_inner
template<typename mint>
struct NTT
{
    static constexpr uint32_t mod = mint::get_mod();
    static constexpr uint32_t pr = ntt_inner::get_pr(mint::get_mod());
    static constexpr int level = __builtin_ctzll(mod - 1);
    mint dw[level], dy[level];
    mint *buf1, *buf2;
    constexpr NTT()
    {
        setwy(level);
        union raw_cast
        {
            mint dat;
            uint32_t _;
        };
        buf1 = &(((raw_cast*)(ntt_inner::_buf1))->dat);
        buf2 = &(((raw_cast*)(ntt_inner::_buf2))->dat);
    }
    constexpr 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[0] = dy[0] = w[1] * w[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];
        }
    }
    __attribute__((target("avx2"))) void ntt(mint* a, int n)
    {
        int k = n ? __builtin_ctz(n) : 0;
        if (k == 0) 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);
            if (v < 8) {
                for (int j = 0; j < v; ++j) {
                    mint ajv = a[j + v];
                    a[j + v] = a[j] - ajv;
                    a[j] += ajv;
                }
            } else {
                const __m256i m0 = _mm256_set1_epi32(0);
                const __m256i m2 = _mm256_set1_epi32(mod + mod);
                int j0 = 0;
                int j1 = v;
                for (; j0 < v; j0 += 8, j1 += 8) {
                    __m256i T0 = _mm256_loadu_si256((__m256i*)(a + j0));
                    __m256i T1 = _mm256_loadu_si256((__m256i*)(a + j1));
                    __m256i naj = montgomery_add_256(T0, T1, m2, m0);
                    __m256i najv = montgomery_sub_256(T0, T1, m2, m0);
                    _mm256_storeu_si256((__m256i*)(a + j0), naj);
                    _mm256_storeu_si256((__m256i*)(a + j1), najv);
                }
            }
        }
        int u = 1 << (2 + (k & 1));
        int v = 1 << (k - 2 - (k & 1));
        mint one = mint(1);
        mint imag = dw[1];
        while (v) {
            if (v == 1) {
                mint ww = one, xx = one, wx = one;
                for (int jh = 0; jh < u;) {
                    ww = xx * xx, wx = ww * xx;
                    mint t0 = a[jh + 0], t1 = a[jh + 1] * xx;
                    mint t2 = a[jh + 2] * ww, t3 = a[jh + 3] * wx;
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[jh + 0] = t0p2 + t1p3, a[jh + 1] = t0p2 - t1p3;
                    a[jh + 2] = t0m2 + t1m3, a[jh + 3] = t0m2 - t1m3;
                    xx *= dw[__builtin_ctz((jh += 4))];
                }
            } else if (v == 4) {
                const __m128i m0 = _mm_set1_epi32(0);
                const __m128i m1 = _mm_set1_epi32(mod);
                const __m128i m2 = _mm_set1_epi32(mod + mod);
                const __m128i r = _mm_set1_epi32(mint::r);
                const __m128i Imag = _mm_set1_epi32(imag.a);
                mint ww = one, xx = one, wx = one;
                for (int jh = 0; jh < u;) {
                    if (jh == 0) {
                        int j0 = 0;
                        int j1 = v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = v;
                        for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
                            const __m128i T0
                                = _mm_loadu_si128((__m128i*)(a + j0));
                            const __m128i T1
                                = _mm_loadu_si128((__m128i*)(a + j1));
                            const __m128i T2
                                = _mm_loadu_si128((__m128i*)(a + j2));
                            const __m128i T3
                                = _mm_loadu_si128((__m128i*)(a + j3));
                            const __m128i T0P2
                                = montgomery_add_128(T0, T2, m2, m0);
                            const __m128i T1P3
                                = montgomery_add_128(T1, T3, m2, m0);
                            const __m128i T0M2
                                = montgomery_sub_128(T0, T2, m2, m0);
                            const __m128i T1M3 = montgomery_mul_128(
                                montgomery_sub_128(T1, T3, m2, m0),
                                Imag,
                                r,
                                m1);
                            _mm_storeu_si128(
                                (__m128i*)(a + j0),
                                montgomery_add_128(T0P2, T1P3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j1),
                                montgomery_sub_128(T0P2, T1P3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j2),
                                montgomery_add_128(T0M2, T1M3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j3),
                                montgomery_sub_128(T0M2, T1M3, m2, m0));
                        }
                    } else {
                        ww = xx * xx, wx = ww * xx;
                        const __m128i WW = _mm_set1_epi32(ww.a);
                        const __m128i WX = _mm_set1_epi32(wx.a);
                        const __m128i XX = _mm_set1_epi32(xx.a);
                        int j0 = jh * v;
                        int j1 = j0 + v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = j1;
                        for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
                            const __m128i T0
                                = _mm_loadu_si128((__m128i*)(a + j0));
                            const __m128i T1
                                = _mm_loadu_si128((__m128i*)(a + j1));
                            const __m128i T2
                                = _mm_loadu_si128((__m128i*)(a + j2));
                            const __m128i T3
                                = _mm_loadu_si128((__m128i*)(a + j3));
                            const __m128i MT1
                                = montgomery_mul_128(T1, XX, r, m1);
                            const __m128i MT2
                                = montgomery_mul_128(T2, WW, r, m1);
                            const __m128i MT3
                                = montgomery_mul_128(T3, WX, r, m1);
                            const __m128i T0P2
                                = montgomery_add_128(T0, MT2, m2, m0);
                            const __m128i T1P3
                                = montgomery_add_128(MT1, MT3, m2, m0);
                            const __m128i T0M2
                                = montgomery_sub_128(T0, MT2, m2, m0);
                            const __m128i T1M3 = montgomery_mul_128(
                                montgomery_sub_128(MT1, MT3, m2, m0),
                                Imag,
                                r,
                                m1);
                            _mm_storeu_si128(
                                (__m128i*)(a + j0),
                                montgomery_add_128(T0P2, T1P3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j1),
                                montgomery_sub_128(T0P2, T1P3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j2),
                                montgomery_add_128(T0M2, T1M3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j3),
                                montgomery_sub_128(T0M2, T1M3, m2, m0));
                        }
                    }
                    xx *= dw[__builtin_ctz((jh += 4))];
                }
            } else {
                const __m256i m0 = _mm256_set1_epi32(0);
                const __m256i m1 = _mm256_set1_epi32(mod);
                const __m256i m2 = _mm256_set1_epi32(mod + mod);
                const __m256i r = _mm256_set1_epi32(mint::r);
                const __m256i Imag = _mm256_set1_epi32(imag.a);
                mint ww = one, xx = one, wx = one;
                for (int jh = 0; jh < u;) {
                    if (jh == 0) {
                        int j0 = 0;
                        int j1 = v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = v;
                        for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
                            const __m256i T0
                                = _mm256_loadu_si256((__m256i*)(a + j0));
                            const __m256i T1
                                = _mm256_loadu_si256((__m256i*)(a + j1));
                            const __m256i T2
                                = _mm256_loadu_si256((__m256i*)(a + j2));
                            const __m256i T3
                                = _mm256_loadu_si256((__m256i*)(a + j3));
                            const __m256i T0P2
                                = montgomery_add_256(T0, T2, m2, m0);
                            const __m256i T1P3
                                = montgomery_add_256(T1, T3, m2, m0);
                            const __m256i T0M2
                                = montgomery_sub_256(T0, T2, m2, m0);
                            const __m256i T1M3 = montgomery_mul_256(
                                montgomery_sub_256(T1, T3, m2, m0),
                                Imag,
                                r,
                                m1);
                            _mm256_storeu_si256(
                                (__m256i*)(a + j0),
                                montgomery_add_256(T0P2, T1P3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j1),
                                montgomery_sub_256(T0P2, T1P3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j2),
                                montgomery_add_256(T0M2, T1M3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j3),
                                montgomery_sub_256(T0M2, T1M3, m2, m0));
                        }
                    } else {
                        ww = xx * xx, wx = ww * xx;
                        const __m256i WW = _mm256_set1_epi32(ww.a);
                        const __m256i WX = _mm256_set1_epi32(wx.a);
                        const __m256i XX = _mm256_set1_epi32(xx.a);
                        int j0 = jh * v;
                        int j1 = j0 + v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = j1;
                        for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
                            const __m256i T0
                                = _mm256_loadu_si256((__m256i*)(a + j0));
                            const __m256i T1
                                = _mm256_loadu_si256((__m256i*)(a + j1));
                            const __m256i T2
                                = _mm256_loadu_si256((__m256i*)(a + j2));
                            const __m256i T3
                                = _mm256_loadu_si256((__m256i*)(a + j3));
                            const __m256i MT1
                                = montgomery_mul_256(T1, XX, r, m1);
                            const __m256i MT2
                                = montgomery_mul_256(T2, WW, r, m1);
                            const __m256i MT3
                                = montgomery_mul_256(T3, WX, r, m1);
                            const __m256i T0P2
                                = montgomery_add_256(T0, MT2, m2, m0);
                            const __m256i T1P3
                                = montgomery_add_256(MT1, MT3, m2, m0);
                            const __m256i T0M2
                                = montgomery_sub_256(T0, MT2, m2, m0);
                            const __m256i T1M3 = montgomery_mul_256(
                                montgomery_sub_256(MT1, MT3, m2, m0),
                                Imag,
                                r,
                                m1);
                            _mm256_storeu_si256(
                                (__m256i*)(a + j0),
                                montgomery_add_256(T0P2, T1P3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j1),
                                montgomery_sub_256(T0P2, T1P3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j2),
                                montgomery_add_256(T0M2, T1M3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j3),
                                montgomery_sub_256(T0M2, T1M3, m2, m0));
                        }
                    }
                    xx *= dw[__builtin_ctz((jh += 4))];
                }
            }
            u <<= 2;
            v >>= 2;
        }
    }
    __attribute__((target("avx2"))) void
        intt(mint* a, int n, int normalize = true)
    {
        int k = n ? __builtin_ctz(n) : 0;
        if (k == 0) return;
        if (k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            if (normalize) {
                a[0] *= mint(2).inverse();
                a[1] *= mint(2).inverse();
            }
            return;
        }
        int u = 1 << (k - 2);
        int v = 1;
        mint one = mint(1);
        mint imag = dy[1];
        while (u) {
            if (v == 1) {
                mint ww = one, xx = one, yy = one;
                u <<= 2;
                for (int jh = 0; jh < u;) {
                    ww = xx * xx, yy = xx * imag;
                    mint t0 = a[jh + 0], t1 = a[jh + 1];
                    mint t2 = a[jh + 2], t3 = a[jh + 3];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
                    a[jh + 0] = t0p1 + t2p3, a[jh + 2] = (t0p1 - t2p3) * ww;
                    a[jh + 1] = t0m1 + t2m3, a[jh + 3] = (t0m1 - t2m3) * ww;
                    xx *= dy[__builtin_ctz(jh += 4)];
                }
            } else if (v == 4) {
                const __m128i m0 = _mm_set1_epi32(0);
                const __m128i m1 = _mm_set1_epi32(mod);
                const __m128i m2 = _mm_set1_epi32(mod + mod);
                const __m128i r = _mm_set1_epi32(mint::r);
                const __m128i Imag = _mm_set1_epi32(imag.a);
                mint ww = one, xx = one, yy = one;
                u <<= 2;
                for (int jh = 0; jh < u;) {
                    if (jh == 0) {
                        int j0 = 0;
                        int j1 = v;
                        int j2 = v + v;
                        int j3 = j2 + v;
                        for (; j0 < v; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
                            const __m128i T0
                                = _mm_loadu_si128((__m128i*)(a + j0));
                            const __m128i T1
                                = _mm_loadu_si128((__m128i*)(a + j1));
                            const __m128i T2
                                = _mm_loadu_si128((__m128i*)(a + j2));
                            const __m128i T3
                                = _mm_loadu_si128((__m128i*)(a + j3));
                            const __m128i T0P1
                                = montgomery_add_128(T0, T1, m2, m0);
                            const __m128i T2P3
                                = montgomery_add_128(T2, T3, m2, m0);
                            const __m128i T0M1
                                = montgomery_sub_128(T0, T1, m2, m0);
                            const __m128i T2M3 = montgomery_mul_128(
                                montgomery_sub_128(T2, T3, m2, m0),
                                Imag,
                                r,
                                m1);
                            _mm_storeu_si128(
                                (__m128i*)(a + j0),
                                montgomery_add_128(T0P1, T2P3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j2),
                                montgomery_sub_128(T0P1, T2P3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j1),
                                montgomery_add_128(T0M1, T2M3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j3),
                                montgomery_sub_128(T0M1, T2M3, m2, m0));
                        }
                    } else {
                        ww = xx * xx, yy = xx * imag;
                        const __m128i WW = _mm_set1_epi32(ww.a);
                        const __m128i XX = _mm_set1_epi32(xx.a);
                        const __m128i YY = _mm_set1_epi32(yy.a);
                        int j0 = jh * v;
                        int j1 = j0 + v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = j1;
                        for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
                            const __m128i T0
                                = _mm_loadu_si128((__m128i*)(a + j0));
                            const __m128i T1
                                = _mm_loadu_si128((__m128i*)(a + j1));
                            const __m128i T2
                                = _mm_loadu_si128((__m128i*)(a + j2));
                            const __m128i T3
                                = _mm_loadu_si128((__m128i*)(a + j3));
                            const __m128i T0P1
                                = montgomery_add_128(T0, T1, m2, m0);
                            const __m128i T2P3
                                = montgomery_add_128(T2, T3, m2, m0);
                            const __m128i T0M1 = montgomery_mul_128(
                                montgomery_sub_128(T0, T1, m2, m0), XX, r, m1);
                            __m128i T2M3 = montgomery_mul_128(
                                montgomery_sub_128(T2, T3, m2, m0), YY, r, m1);
                            _mm_storeu_si128(
                                (__m128i*)(a + j0),
                                montgomery_add_128(T0P1, T2P3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j2),
                                montgomery_mul_128(
                                    montgomery_sub_128(T0P1, T2P3, m2, m0),
                                    WW,
                                    r,
                                    m1));
                            _mm_storeu_si128(
                                (__m128i*)(a + j1),
                                montgomery_add_128(T0M1, T2M3, m2, m0));
                            _mm_storeu_si128(
                                (__m128i*)(a + j3),
                                montgomery_mul_128(
                                    montgomery_sub_128(T0M1, T2M3, m2, m0),
                                    WW,
                                    r,
                                    m1));
                        }
                    }
                    xx *= dy[__builtin_ctz(jh += 4)];
                }
            } else {
                const __m256i m0 = _mm256_set1_epi32(0);
                const __m256i m1 = _mm256_set1_epi32(mod);
                const __m256i m2 = _mm256_set1_epi32(mod + mod);
                const __m256i r = _mm256_set1_epi32(mint::r);
                const __m256i Imag = _mm256_set1_epi32(imag.a);
                mint ww = one, xx = one, yy = one;
                u <<= 2;
                for (int jh = 0; jh < u;) {
                    if (jh == 0) {
                        int j0 = 0;
                        int j1 = v;
                        int j2 = v + v;
                        int j3 = j2 + v;
                        for (; j0 < v; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
                            const __m256i T0
                                = _mm256_loadu_si256((__m256i*)(a + j0));
                            const __m256i T1
                                = _mm256_loadu_si256((__m256i*)(a + j1));
                            const __m256i T2
                                = _mm256_loadu_si256((__m256i*)(a + j2));
                            const __m256i T3
                                = _mm256_loadu_si256((__m256i*)(a + j3));
                            const __m256i T0P1
                                = montgomery_add_256(T0, T1, m2, m0);
                            const __m256i T2P3
                                = montgomery_add_256(T2, T3, m2, m0);
                            const __m256i T0M1
                                = montgomery_sub_256(T0, T1, m2, m0);
                            const __m256i T2M3 = montgomery_mul_256(
                                montgomery_sub_256(T2, T3, m2, m0),
                                Imag,
                                r,
                                m1);
                            _mm256_storeu_si256(
                                (__m256i*)(a + j0),
                                montgomery_add_256(T0P1, T2P3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j2),
                                montgomery_sub_256(T0P1, T2P3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j1),
                                montgomery_add_256(T0M1, T2M3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j3),
                                montgomery_sub_256(T0M1, T2M3, m2, m0));
                        }
                    } else {
                        ww = xx * xx, yy = xx * imag;
                        const __m256i WW = _mm256_set1_epi32(ww.a);
                        const __m256i XX = _mm256_set1_epi32(xx.a);
                        const __m256i YY = _mm256_set1_epi32(yy.a);
                        int j0 = jh * v;
                        int j1 = j0 + v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = j1;
                        for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
                            const __m256i T0
                                = _mm256_loadu_si256((__m256i*)(a + j0));
                            const __m256i T1
                                = _mm256_loadu_si256((__m256i*)(a + j1));
                            const __m256i T2
                                = _mm256_loadu_si256((__m256i*)(a + j2));
                            const __m256i T3
                                = _mm256_loadu_si256((__m256i*)(a + j3));
                            const __m256i T0P1
                                = montgomery_add_256(T0, T1, m2, m0);
                            const __m256i T2P3
                                = montgomery_add_256(T2, T3, m2, m0);
                            const __m256i T0M1 = montgomery_mul_256(
                                montgomery_sub_256(T0, T1, m2, m0), XX, r, m1);
                            const __m256i T2M3 = montgomery_mul_256(
                                montgomery_sub_256(T2, T3, m2, m0), YY, r, m1);
                            _mm256_storeu_si256(
                                (__m256i*)(a + j0),
                                montgomery_add_256(T0P1, T2P3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j2),
                                montgomery_mul_256(
                                    montgomery_sub_256(T0P1, T2P3, m2, m0),
                                    WW,
                                    r,
                                    m1));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j1),
                                montgomery_add_256(T0M1, T2M3, m2, m0));
                            _mm256_storeu_si256(
                                (__m256i*)(a + j3),
                                montgomery_mul_256(
                                    montgomery_sub_256(T0M1, T2M3, m2, m0),
                                    WW,
                                    r,
                                    m1));
                        }
                    }
                    xx *= dy[__builtin_ctz(jh += 4)];
                }
            }
            u >>= 4;
            v <<= 2;
        }
        if (k & 1) {
            v = 1 << (k - 1);
            if (v < 8) {
                for (int j = 0; j < v; ++j) {
                    mint ajv = a[j] - a[j + v];
                    a[j] += a[j + v];
                    a[j + v] = ajv;
                }
            } else {
                const __m256i m0 = _mm256_set1_epi32(0);
                const __m256i m2 = _mm256_set1_epi32(mod + mod);
                int j0 = 0;
                int j1 = v;
                for (; j0 < v; j0 += 8, j1 += 8) {
                    const __m256i T0 = _mm256_loadu_si256((__m256i*)(a + j0));
                    const __m256i T1 = _mm256_loadu_si256((__m256i*)(a + j1));
                    __m256i naj = montgomery_add_256(T0, T1, m2, m0);
                    __m256i najv = montgomery_sub_256(T0, T1, m2, m0);
                    _mm256_storeu_si256((__m256i*)(a + j0), naj);
                    _mm256_storeu_si256((__m256i*)(a + j1), najv);
                }
            }
        }
        if (normalize) {
            mint invn = mint(n).inverse();
            for (int i = 0; i < n; i++)
                a[i] *= invn;
        }
    }
    __attribute__((target("avx2"))) void
        inplace_multiply(int l1, int l2, int zero_padding = true)
    {
        int l = l1 + l2 - 1;
        int M = 4;
        while (M < l)
            M <<= 1;
        if (zero_padding) {
            for (int i = l1; i < M; i++)
                ntt_inner::_buf1[i] = 0;
            for (int i = l2; i < M; i++)
                ntt_inner::_buf2[i] = 0;
        }
        const __m256i m0 = _mm256_set1_epi32(0);
        const __m256i m1 = _mm256_set1_epi32(mod);
        const __m256i r = _mm256_set1_epi32(mint::r);
        const __m256i N2 = _mm256_set1_epi32(mint::n2);
        for (int i = 0; i < l1; i += 8) {
            __m256i a = _mm256_loadu_si256((__m256i*)(ntt_inner::_buf1 + i));
            __m256i b = montgomery_mul_256(a, N2, r, m1);
            _mm256_storeu_si256((__m256i*)(ntt_inner::_buf1 + i), b);
        }
        for (int i = 0; i < l2; i += 8) {
            __m256i a = _mm256_loadu_si256((__m256i*)(ntt_inner::_buf2 + i));
            __m256i b = montgomery_mul_256(a, N2, r, m1);
            _mm256_storeu_si256((__m256i*)(ntt_inner::_buf2 + i), b);
        }
        ntt(buf1, M);
        ntt(buf2, M);
        for (int i = 0; i < M; i += 8) {
            __m256i a = _mm256_loadu_si256((__m256i*)(ntt_inner::_buf1 + i));
            __m256i b = _mm256_loadu_si256((__m256i*)(ntt_inner::_buf2 + i));
            __m256i c = montgomery_mul_256(a, b, r, m1);
            _mm256_storeu_si256((__m256i*)(ntt_inner::_buf1 + i), c);
        }
        intt(buf1, M, false);
        const __m256i INVM = _mm256_set1_epi32((mint(M).inverse()).a);
        for (int i = 0; i < l; i += 8) {
            __m256i a = _mm256_loadu_si256((__m256i*)(ntt_inner::_buf1 + i));
            __m256i b = montgomery_mul_256(a, INVM, r, m1);
            __m256i c = my256_mulhi_epu32(my256_mullo_epu32(b, r), m1);
            __m256i d = _mm256_and_si256(_mm256_cmpgt_epi32(c, m0), m1);
            __m256i e = _mm256_sub_epi32(d, c);
            _mm256_storeu_si256((__m256i*)(ntt_inner::_buf1 + i), e);
        }
    }
    void ntt(Vec<mint>& a)
    {
        int M = (int)a.size();
        for (int i = 0; i < M; i++)
            buf1[i].a = a[i].a;
        ntt(buf1, M);
        for (int i = 0; i < M; i++)
            a[i].a = buf1[i].a;
    }
    void intt(Vec<mint>& a)
    {
        int M = (int)a.size();
        for (int i = 0; i < M; i++)
            buf1[i].a = a[i].a;
        intt(buf1, M, true);
        for (int i = 0; i < M; i++)
            a[i].a = buf1[i].a;
    }
    Vec<mint> multiply(const Vec<mint>& a, const Vec<mint>& b)
    {
        if (a.size() == 0 && b.size() == 0) return Vec<mint>{};
        int l = a.size() + b.size() - 1;
        if (std::min<int>(a.size(), b.size()) <= 40) {
            Vec<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;
        }
        assert(l <= ntt_inner::SZ_FFT_BUF);
        int M = 4;
        while (M < l)
            M <<= 1;
        for (int i = 0; i < (int)a.size(); ++i)
            buf1[i].a = a[i].a;
        for (int i = (int)a.size(); i < M; ++i)
            buf1[i].a = 0;
        for (int i = 0; i < (int)b.size(); ++i)
            buf2[i].a = b[i].a;
        for (int i = (int)b.size(); i < M; ++i)
            buf2[i].a = 0;
        ntt(buf1, M);
        ntt(buf2, M);
        for (int i = 0; i < M; ++i)
            buf1[i].a = mint::reduce(uint64_t(buf1[i].a) * buf2[i].a);
        intt(buf1, M, false);
        Vec<mint> s(l);
        mint invm = mint(M).inverse();
        for (int i = 0; i < l; ++i)
            s[i] = buf1[i] * invm;
        return s;
    }
    void ntt_doubling(Vec<mint>& a)
    {
        int M = (int)a.size();
        for (int i = 0; i < M; i++)
            buf1[i].a = a[i].a;
        intt(buf1, M);
        mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
        for (int i = 0; i < M; i++)
            buf1[i] *= r, r *= zeta;
        ntt(buf1, M);
        a.resize(2 * M);
        for (int i = 0; i < M; i++)
            a[M + i].a = buf1[i].a;
    }
};
template<typename mint>
struct FormalPowerSeries : Vec<mint>
{
    using Vec<mint>::Vec;
    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) 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 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();
    }
    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;
/**
 * @brief 多項式/形式的冪級数ライブラリ
 * @docs docs/fps/formal-power-series.md
 */
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;
}
/**
 * @brief NTT mod用FPSライブラリ
 * @docs docs/fps/ntt-friendly-fps.md
 */
template<typename fps>
fps multivariate_multiplication(const fps& f,
                                const fps& g,
                                const Vec<int>& base)
{
    int n = f.size(), s = base.size(), W = 1;
    if (s == 0) return fps{f[0] * g[0]};
    while (W < 2 * n)
        W *= 2;
    Vec<int> chi(n);
    for (int i = 0; i < n; i++) {
        int x = i;
        for (int j = 0; j < s - 1; j++)
            chi[i] += (x /= base[j]);
        chi[i] %= s;
    }
    Vec<fps> F(s, fps(W)), G(s, fps(W));
    for (int i = 0; i < n; i++)
        F[chi[i]][i] = f[i], G[chi[i]][i] = g[i];
    for (auto& x : F)
        x.ntt();
    for (auto& x : G)
        x.ntt();
    fps a(s);
    for (int k = 0; k < W; k++) {
        fill(begin(a), end(a), typename fps::value_type());
        for (int i = 0; i < s; i++)
            for (int j = 0; j < s; j++) {
                a[i + j - (i + j >= s ? s : 0)] += F[i][k] * G[j][k];
            }
        for (int i = 0; i < s; i++)
            F[i][k] = a[i];
    }
    for (auto& x : F)
        x.intt();
    fps h(n);
    for (int i = 0; i < n; i++)
        h[i] = F[chi[i]][i];
    return h;
}
/**
 * @brief Multivariate Multiplication
 * @docs docs/ntt/multivariate-multiplication.md
 */
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(r * mod == 1, "invalid, r * mod != 1");
    static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
    static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
    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 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
    {
        return pow(mod - 2);
    }
    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;
    }
};
constexpr u32 MOD = (1 << 20) * 115 + 1; // 120586241
using mint = LazyMontgomeryModInt<MOD>;
using fps = FormalPowerSeries<mint>;
int main()
{
    const auto [N, K, M, T] = in.tup<int, int, i64, int>();
    const auto as = in.vec<int>(N);
    Vec<int> ns(K);
    for (int i : rep(K)) {
        if (i < T) {
            ns[i] = 10;
        } else {
            ns[i] = 20;
        }
    }
    Vec<int> p10s(K + 1, 1);
    Vec<int> p20s(K + 1, 1);
    for (int i : rep(K)) {
        p10s[i + 1] = p10s[i] * 10;
        p20s[i + 1] = p20s[i] * 20;
    }
    const int B1 = p10s[T];
    const int B2 = p20s[K - T];
    auto d2x = [&, K = K, T = T](
                   int D) -> int { // dは10進数,xは(20,20,...,10,10,...)進数
        int X = 0;
        int B = 1;
        for (int i : rep(K)) {
            const int dig = (i < T ? 10 : 20);
            X += (D % 10) * B;
            D /= 10;
            B *= dig;
        }
        return X;
    };
    auto x2d = [&, K = K, T = T](int X) -> Pair<bool, int> {
        int D = 0;
        for (int i : rep(K)) {
            const int dig = (i < T ? 10 : 20);
            if (X % dig >= 10) { return {false, 0}; }
            D += p10s[i] * (X % dig);
            X /= dig;
        }
        return {true, D};
    };
    auto mul = [&, K = K, T = T](const fps& f, const fps& g) {
        auto h = multivariate_multiplication(f, g, ns);
        for (int n2 : rep(B2)) {
            int tmp = n2;
            int nn2 = 0;
            for (int i : rep(K - T)) {
                int d = tmp % 20;
                tmp /= 20;
                nn2 += (d % 10) * p20s[i];
            }
            if (n2 == nn2) { continue; }
            for (int n1 : rep(B1)) {
                h[nn2 * B1 + n1] += h[n2 * B1 + n1];
                h[n2 * B1 + n1] = 0;
            }
        }
        void(0);
        return h;
    };
    auto power = Fix([&](auto dfs, const fps& f, const i64 M) -> fps {
        if (M == 1) {
            return f;
        } else if (M % 2 == 0) {
            return dfs(mul(f, f), M / 2);
        } else {
            return mul(dfs(f, M - 1), f);
        }
    });
    fps f(B2 * B1, 0);
    for (int i : rep(N)) {
        f[d2x(as[i])] += 1;
    }
    Vec<mint> ans(p10s[K]);
    const auto dp = power(f, M);
    for (int i : rep(B1 * B2)) {
        const auto [b, j] = x2d(i);
        if (b) { ans[j] += dp[i]; }
    }
    for (int i : rep(p10s[K])) {
        out.ln(ans[i]);
    }
    return 0;
}