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#130851#618. 多项式乘法GoatGirl98#Compile Error//C1143.5kb2023-07-25 14:10:132023-07-25 14:10:17

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  • [2023-08-10 23:21:45]
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answer

// Polynomial test From HOS
#include <assert.h>
#include <string.h>
#include <algorithm>
#include <initializer_list>
#include <vector>

#ifndef LIBRA_ALGEBRA_FFT_998244353_H_
#define LIBRA_ALGEBRA_FFT_998244353_H_

#include <assert.h>
#include <vector>

#ifndef LIBRA_ALGEBRA_MODINT_H_
#define LIBRA_ALGEBRA_MODINT_H_

#include <stdio.h>
typedef long long ll;
namespace FastIO
{
    char buf[1 << 21], *p1 = buf, *p2 = buf;
    inline char nc() { return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 21, stdin), p1 == p2) ? EOF : *p1++; }
    ll rd()
    {
        ll ret = 0, f = 1;
        char ch = nc();

        while (ch < '0' || ch > '9')
        {
            if (ch == '-')
                f = -1;
            ch = nc();
        }
        while (ch >= '0' && ch <= '9')
        {
            ret = (ret << 1) + (ret << 3) + (ch ^ 48);
            ch = nc();
        }

        return f == 1 ? ret : -ret;
    }
    char Buf[1 << 21], out[20];
    int P, out_size;
    void flush() { fwrite(Buf, 1, out_size, stdout), out_size = 0; }
    void wt(ll x, char ch)
    {
        if (out_size >= 1 << 20)
            flush();

        if (x < 0)
            Buf[out_size++] = 45, x = -x;

        do
            out[++P] = (x % 10) ^ 48;
        while (x /= 10);

        do
            Buf[out_size++] = out[P];
        while (--P);
        Buf[out_size++] = ch;
    }
    struct IOFlush
    {
        ~IOFlush() { flush(); }
    } tail;
}

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_>
struct ModInt
{
    static constexpr unsigned M = M_;
    unsigned x;
    constexpr ModInt() : x(0U) {}
    constexpr ModInt(unsigned x_) : x(x_ % M) {}
    constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
    constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
    constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
    ModInt &operator+=(const ModInt &a)
    {
        x = ((x += a.x) >= M) ? (x - M) : x;
        return *this;
    }
    ModInt &operator-=(const ModInt &a)
    {
        x = ((x -= a.x) >= M) ? (x + M) : x;
        return *this;
    }
    ModInt &operator*=(const ModInt &a)
    {
        x = (static_cast<unsigned long long>(x) * a.x) % M;
        return *this;
    }
    ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
    ModInt pow(long long e) const
    {
        if (e < 0)
            return inv().pow(-e);
        ModInt a = *this, b = 1U;
        for (; e; e >>= 1)
        {
            if (e & 1)
                b *= a;
            a *= a;
        }
        return b;
    }
    ModInt inv() const
    {
        unsigned a = M, b = x;
        int y = 0, z = 1;
        for (; b;)
        {
            const unsigned q = a / b;
            const unsigned c = a - q * b;
            a = b;
            b = c;
            const int w = y - static_cast<int>(q) * z;
            y = z;
            z = w;
        }
        assert(a == 1U);
        return ModInt(y);
    }
    ModInt operator+() const { return *this; }
    ModInt operator-() const
    {
        ModInt a;
        a.x = x ? (M - x) : 0U;
        return a;
    }
    ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
    ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
    ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
    ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
    template <class T>
    friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
    template <class T>
    friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
    template <class T>
    friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
    template <class T>
    friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
    explicit operator bool() const { return x; }
    bool operator==(const ModInt &a) const { return (x == a.x); }
    bool operator!=(const ModInt &a) const { return (x != a.x); }
    // friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

#endif // LIBRA_ALGEBRA_MODINT_H_

using std::vector;

////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353U;
constexpr unsigned MO2 = 2U * MO;
constexpr int FFT_MAX = 23;
using Mint = ModInt<MO>;
constexpr Mint FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U, 166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U, 733596141U, 267099868U, 15311432U};
constexpr Mint INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U, 685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U, 428961804U, 382752275U, 469870224U};
constexpr Mint FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U, 856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U, 867605899U};
constexpr Mint INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U, 90816748U, 860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U, 824071951U, 103369235U};

// as[rev(i)] <- \sum_j \zeta^(ij) as[j]
void fft(Mint *as, int n)
{
    assert(!(n & (n - 1)));
    assert(1 <= n);
    assert(n <= 1 << FFT_MAX);
    int m = n;
    if (m >>= 1)
    {
        for (int i = 0; i < m; ++i)
        {
            const unsigned x = as[i + m].x; // < MO
            as[i + m].x = as[i].x + MO - x; // < 2 MO
            as[i].x += x;                   // < 2 MO
        }
    }
    if (m >>= 1)
    {
        Mint prod = 1U;
        for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1))
        {
            for (int i = i0; i < i0 + m; ++i)
            {
                const unsigned x = (prod * as[i + m]).x; // < MO
                as[i + m].x = as[i].x + MO - x;          // < 3 MO
                as[i].x += x;                            // < 3 MO
            }
            prod *= FFT_RATIOS[__builtin_ctz(++h)];
        }
    }
    for (; m;)
    {
        if (m >>= 1)
        {
            Mint prod = 1U;
            for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1))
            {
                for (int i = i0; i < i0 + m; ++i)
                {
                    const unsigned x = (prod * as[i + m]).x; // < MO
                    as[i + m].x = as[i].x + MO - x;          // < 4 MO
                    as[i].x += x;                            // < 4 MO
                }
                prod *= FFT_RATIOS[__builtin_ctz(++h)];
            }
        }
        if (m >>= 1)
        {
            Mint prod = 1U;
            for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1))
            {
                for (int i = i0; i < i0 + m; ++i)
                {
                    const unsigned x = (prod * as[i + m]).x;                // < MO
                    as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MO
                    as[i + m].x = as[i].x + MO - x;                         // < 3 MO
                    as[i].x += x;                                           // < 3 MO
                }
                prod *= FFT_RATIOS[__builtin_ctz(++h)];
            }
        }
    }
    for (int i = 0; i < n; ++i)
    {
        as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MO
        as[i].x = (as[i].x >= MO) ? (as[i].x - MO) : as[i].x;   // < MO
    }
}

// as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]
void invFft(Mint *as, int n)
{
    assert(!(n & (n - 1)));
    assert(1 <= n);
    assert(n <= 1 << FFT_MAX);
    int m = 1;
    if (m < n >> 1)
    {
        Mint prod = 1U;
        for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1))
        {
            for (int i = i0; i < i0 + m; ++i)
            {
                const unsigned long long y = as[i].x + MO - as[i + m].x; // < 2 MO
                as[i].x += as[i + m].x;                                  // < 2 MO
                as[i + m].x = (prod.x * y) % MO;                         // < MO
            }
            prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
        }
        m <<= 1;
    }
    for (; m < n >> 1; m <<= 1)
    {
        Mint prod = 1U;
        for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1))
        {
            for (int i = i0; i < i0 + (m >> 1); ++i)
            {
                const unsigned long long y = as[i].x + MO2 - as[i + m].x; // < 4 MO
                as[i].x += as[i + m].x;                                   // < 4 MO
                as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;   // < 2 MO
                as[i + m].x = (prod.x * y) % MO;                          // < MO
            }
            for (int i = i0 + (m >> 1); i < i0 + m; ++i)
            {
                const unsigned long long y = as[i].x + MO - as[i + m].x; // < 2 MO
                as[i].x += as[i + m].x;                                  // < 2 MO
                as[i + m].x = (prod.x * y) % MO;                         // < MO
            }
            prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
        }
    }
    if (m < n)
    {
        for (int i = 0; i < m; ++i)
        {
            const unsigned y = as[i].x + MO2 - as[i + m].x; // < 4 MO
            as[i].x += as[i + m].x;                         // < 4 MO
            as[i + m].x = y;                                // < 4 MO
        }
    }
    const Mint invN = Mint(n).inv();
    for (int i = 0; i < n; ++i)
    {
        as[i] *= invN;
    }
}

void fft(vector<Mint> &as)
{
    fft(as.data(), as.size());
}
void invFft(vector<Mint> &as)
{
    invFft(as.data(), as.size());
}

vector<Mint> convolve(vector<Mint> as, vector<Mint> bs)
{
    if (as.empty() || bs.empty())
        return {};
    const int len = as.size() + bs.size() - 1;
    int n = 1;
    for (; n < len; n <<= 1)
    {
    }
    as.resize(n);
    fft(as);
    bs.resize(n);
    fft(bs);
    for (int i = 0; i < n; ++i)
        as[i] *= bs[i];
    invFft(as);
    as.resize(len);
    return as;
}
vector<Mint> square(vector<Mint> as)
{
    if (as.empty())
        return {};
    const int len = as.size() + as.size() - 1;
    int n = 1;
    for (; n < len; n <<= 1)
    {
    }
    as.resize(n);
    fft(as);
    for (int i = 0; i < n; ++i)
        as[i] *= as[i];
    invFft(as);
    as.resize(len);
    return as;
}
////////////////////////////////////////////////////////////////////////////////

#endif // LIBRA_ALGEBRA_FFT_998244353_H_

using std::max;
using std::min;
using std::vector;

////////////////////////////////////////////////////////////////////////////////
// inv: log, exp, pow
// fac: shift
// invFac: shift
constexpr int LIM_INV = 1 << 20; // @
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];
struct ModIntPreparator
{
    ModIntPreparator()
    {
        inv[1] = 1;
        for (int i = 2; i < LIM_INV; ++i)
            inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
        fac[0] = 1;
        for (int i = 1; i < LIM_INV; ++i)
            fac[i] = fac[i - 1] * i;
        invFac[0] = 1;
        for (int i = 1; i < LIM_INV; ++i)
            invFac[i] = invFac[i - 1] * inv[i];
    }
} preparator;

// polyWork0: *, inv, div, divAt, log, exp, pow, sqrt, shift
// polyWork1: inv, div, divAt, log, exp, pow, sqrt, shift
// polyWork2: divAt, exp, pow, sqrt
// polyWork3: exp, pow, sqrt
static constexpr int LIM_POLY = 1 << 20; // @
static_assert(LIM_POLY <= 1 << FFT_MAX, "Poly: LIM_POLY <= 1 << FFT_MAX must hold.");
static Mint polyWork0[LIM_POLY], polyWork1[LIM_POLY], polyWork2[LIM_POLY], polyWork3[LIM_POLY];

struct Poly : public vector<Mint>
{
    Poly() {}
    explicit Poly(int n) : vector<Mint>(n) {}
    Poly(const vector<Mint> &vec) : vector<Mint>(vec) {}
    Poly(std::initializer_list<Mint> il) : vector<Mint>(il) {}
    int size() const { return vector<Mint>::size(); }
    Mint at(long long k) const { return (0 <= k && k < size()) ? (*this)[k] : 0U; }
    int ord() const
    {
        for (int i = 0; i < size(); ++i)
            if ((*this)[i])
                return i;
        return -1;
    }
    int deg() const
    {
        for (int i = size(); --i >= 0;)
            if ((*this)[i])
                return i;
        return -1;
    }
    Poly mod(int n) const { return Poly(vector<Mint>(data(), data() + min(n, size()))); }
    /*
    friend std::ostream &operator<<(std::ostream &os, const Poly &fs)
    {
        os << "[";
        for (int i = 0; i < fs.size(); ++i)
        {
            if (i > 0)
                os << ", ";
            os << fs[i];
        }
        return os << "]";
    }
    */
    Poly &operator+=(const Poly &fs)
    {
        if (size() < fs.size())
            resize(fs.size());
        for (int i = 0; i < fs.size(); ++i)
            (*this)[i] += fs[i];
        return *this;
    }
    Poly &operator-=(const Poly &fs)
    {
        if (size() < fs.size())
            resize(fs.size());
        for (int i = 0; i < fs.size(); ++i)
            (*this)[i] -= fs[i];
        return *this;
    }
    // 3 E(|t| + |f|)
    Poly &operator*=(const Poly &fs)
    {
        if (empty() || fs.empty())
            return *this = {};
        const int nt = size(), nf = fs.size();
        int n = 1;
        for (; n < nt + nf - 1; n <<= 1)
        {
        }
        assert(n <= LIM_POLY);
        resize(n);
        fft(data(), n); // 1 E(n)
        memcpy(polyWork0, fs.data(), nf * sizeof(Mint));
        memset(polyWork0 + nf, 0, (n - nf) * sizeof(Mint));
        fft(polyWork0, n); // 1 E(n)
        for (int i = 0; i < n; ++i)
            (*this)[i] *= polyWork0[i];
        invFft(data(), n); // 1 E(n)
        resize(nt + nf - 1);
        return *this;
    }
    // 13 E(deg(t) - deg(f) + 1)
    // rev(t) = rev(f) rev(q) + x^(deg(t)-deg(f)+1) rev(r)
    Poly &operator/=(const Poly &fs)
    {
        const int m = deg(), n = fs.deg();
        assert(n != -1);
        if (m < n)
            return *this = {};
        Poly tsRev(m - n + 1), fsRev(min(m - n, n) + 1);
        for (int i = 0; i <= m - n; ++i)
            tsRev[i] = (*this)[m - i];
        for (int i = 0, i0 = min(m - n, n); i <= i0; ++i)
            fsRev[i] = fs[n - i];
        const Poly qsRev = tsRev.div(fsRev, m - n + 1); // 13 E(m - n + 1)
        resize(m - n + 1);
        for (int i = 0; i <= m - n; ++i)
            (*this)[i] = qsRev[m - n - i];
        return *this;
    }
    // 13 E(deg(t) - deg(f) + 1) + 3 E(|t|)
    Poly &operator%=(const Poly &fs)
    {
        const Poly qs = *this / fs; // 13 E(deg(t) - deg(f) + 1)
        *this -= fs * qs;           // 3 E(|t|)
        resize(deg() + 1);
        return *this;
    }
    Poly &operator*=(const Mint &a)
    {
        for (int i = 0; i < size(); ++i)
            (*this)[i] *= a;
        return *this;
    }
    Poly &operator/=(const Mint &a)
    {
        const Mint b = a.inv();
        for (int i = 0; i < size(); ++i)
            (*this)[i] *= b;
        return *this;
    }
    Poly operator+() const { return *this; }
    Poly operator-() const
    {
        Poly fs(size());
        for (int i = 0; i < size(); ++i)
            fs[i] = -(*this)[i];
        return fs;
    }
    Poly operator+(const Poly &fs) const { return (Poly(*this) += fs); }
    Poly operator-(const Poly &fs) const { return (Poly(*this) -= fs); }
    Poly operator*(const Poly &fs) const { return (Poly(*this) *= fs); }
    Poly operator/(const Poly &fs) const { return (Poly(*this) /= fs); }
    Poly operator%(const Poly &fs) const { return (Poly(*this) %= fs); }
    Poly operator*(const Mint &a) const { return (Poly(*this) *= a); }
    Poly operator/(const Mint &a) const { return (Poly(*this) /= a); }
    friend Poly operator*(const Mint &a, const Poly &fs) { return fs * a; }

    // 10 E(n)
    // f <- f - (t f - 1) f
    Poly inv(int n) const
    {
        assert(!empty());
        assert((*this)[0]);
        assert(1 <= n);
        assert(n == 1 || 1 << (32 - __builtin_clz(n - 1)) <= LIM_POLY);
        Poly fs(n);
        fs[0] = (*this)[0].inv();
        for (int m = 1; m < n; m <<= 1)
        {
            memcpy(polyWork0, data(), min(m << 1, size()) * sizeof(Mint));
            memset(polyWork0 + min(m << 1, size()), 0, ((m << 1) - min(m << 1, size())) * sizeof(Mint));
            fft(polyWork0, m << 1); // 2 E(n)
            memcpy(polyWork1, fs.data(), min(m << 1, n) * sizeof(Mint));
            memset(polyWork1 + min(m << 1, n), 0, ((m << 1) - min(m << 1, n)) * sizeof(Mint));
            fft(polyWork1, m << 1); // 2 E(n)
            for (int i = 0; i < m << 1; ++i)
                polyWork0[i] *= polyWork1[i];
            invFft(polyWork0, m << 1); // 2 E(n)
            memset(polyWork0, 0, m * sizeof(Mint));
            fft(polyWork0, m << 1); // 2 E(n)
            for (int i = 0; i < m << 1; ++i)
                polyWork0[i] *= polyWork1[i];
            invFft(polyWork0, m << 1); // 2 E(n)
            for (int i = m, i0 = min(m << 1, n); i < i0; ++i)
                fs[i] = -polyWork0[i];
        }
        return fs;
    }
    // 9 E(n)
    // Need (4 m)-th roots of unity to lift from (mod x^m) to (mod x^(2m)).
    // f <- f - (t f - 1) f
    // (t f^2) mod ((x^(2m) - 1) (x^m - 1^(1/4)))
    /*
    Poly inv(int n) const {
      assert(!empty()); assert((*this)[0]); assert(1 <= n);
      assert(n == 1 || 3 << (31 - __builtin_clz(n - 1)) <= LIM_POLY);
      assert(n <= 1 << (FFT_MAX - 1));
      Poly fs(n);
      fs[0] = (*this)[0].inv();
      for (int h = 2, m = 1; m < n; ++h, m <<= 1) {
        const Mint a = FFT_ROOTS[h], b = INV_FFT_ROOTS[h];
        memcpy(polyWork0, data(), min(m << 1, size()) * sizeof(Mint));
        memset(polyWork0 + min(m << 1, size()), 0, ((m << 1) - min(m << 1, size())) * sizeof(Mint));
        {
          Mint aa = 1;
          for (int i = 0; i < m; ++i) { polyWork0[(m << 1) + i] = aa * polyWork0[i]; aa *= a; }
          for (int i = 0; i < m; ++i) { polyWork0[(m << 1) + i] += aa * polyWork0[m + i]; aa *= a; }
        }
        fft(polyWork0, m << 1);  // 2 E(n)
        fft(polyWork0 + (m << 1), m);  // 1 E(n)
        memcpy(polyWork1, fs.data(), min(m << 1, n) * sizeof(Mint));
        memset(polyWork1 + min(m << 1, n), 0, ((m << 1) - min(m << 1, n)) * sizeof(Mint));
        {
          Mint aa = 1;
          for (int i = 0; i < m; ++i) { polyWork1[(m << 1) + i] = aa * polyWork1[i]; aa *= a; }
          for (int i = 0; i < m; ++i) { polyWork1[(m << 1) + i] += aa * polyWork1[m + i]; aa *= a; }
        }
        fft(polyWork1, m << 1);  // 2 E(n)
        fft(polyWork1 + (m << 1), m);  // 1 E(n)
        for (int i = 0; i < (m << 1) + m; ++i) polyWork0[i] *= polyWork1[i] * polyWork1[i];
        invFft(polyWork0, m << 1);  // 2 E(n)
        invFft(polyWork0 + (m << 1), m);  // 1 E(n)
        // 2 f0 + (-f2), (-f1) + (-f3), 1^(1/4) (-f1) - (-f2) - 1^(1/4) (-f3)
        {
          Mint bb = 1;
          for (int i = 0, i0 = min(m, n - m); i < i0; ++i) {
            unsigned x = polyWork0[i].x + (bb * polyWork0[(m << 1) + i]).x + MO2 - (fs[i].x << 1);  // < 4 MO
            fs[m + i] = Mint(static_cast<unsigned long long>(FFT_ROOTS[2].x) * x) - polyWork0[m + i];
            fs[m + i].x = ((fs[m + i].x & 1) ? (fs[m + i].x + MO) : fs[m + i].x) >> 1;
            bb *= b;
          }
        }
      }
      return fs;
    }
    */
    // 13 E(n)
    // g = (1 / f) mod x^m
    // h <- h - (f h - t) g
    Poly div(const Poly &fs, int n) const
    {
        assert(!fs.empty());
        assert(fs[0]);
        assert(1 <= n);
        if (n == 1)
            return {at(0) / fs[0]};
        // m < n <= 2 m
        const int m = 1 << (31 - __builtin_clz(n - 1));
        assert(m << 1 <= LIM_POLY);
        Poly gs = fs.inv(m); // 5 E(n)
        gs.resize(m << 1);
        fft(gs.data(), m << 1); // 1 E(n)
        memcpy(polyWork0, data(), min(m, size()) * sizeof(Mint));
        memset(polyWork0 + min(m, size()), 0, ((m << 1) - min(m, size())) * sizeof(Mint));
        fft(polyWork0, m << 1); // 1 E(n)
        for (int i = 0; i < m << 1; ++i)
            polyWork0[i] *= gs[i];
        invFft(polyWork0, m << 1); // 1 E(n)
        Poly hs(n);
        memcpy(hs.data(), polyWork0, m * sizeof(Mint));
        memset(polyWork0 + m, 0, m * sizeof(Mint));
        fft(polyWork0, m << 1); // 1 E(n)
        memcpy(polyWork1, fs.data(), min(m << 1, fs.size()) * sizeof(Mint));
        memset(polyWork1 + min(m << 1, fs.size()), 0, ((m << 1) - min(m << 1, fs.size())) * sizeof(Mint));
        fft(polyWork1, m << 1); // 1 E(n)
        for (int i = 0; i < m << 1; ++i)
            polyWork0[i] *= polyWork1[i];
        invFft(polyWork0, m << 1); // 1 E(n)
        memset(polyWork0, 0, m * sizeof(Mint));
        for (int i = m, i0 = min(m << 1, size()); i < i0; ++i)
            polyWork0[i] -= (*this)[i];
        fft(polyWork0, m << 1); // 1 E(n)
        for (int i = 0; i < m << 1; ++i)
            polyWork0[i] *= gs[i];
        invFft(polyWork0, m << 1); // 1 E(n)
        for (int i = m; i < n; ++i)
            hs[i] = -polyWork0[i];
        return hs;
    }
    // (4 (floor(log_2 k) - ceil(log_2 |f|)) + 16) E(|f|)  for  |t| < |f|
    // [x^k] (t(x) / f(x)) = [x^k] ((t(x) f(-x)) / (f(x) f(-x))
    // polyWork0: half of (2 m)-th roots of unity, inversed, bit-reversed
    Mint divAt(const Poly &fs, long long k) const
    {
        assert(k >= 0);
        if (size() >= fs.size())
        {
            const Poly qs = *this / fs; // 13 E(deg(t) - deg(f) + 1)
            Poly rs = *this - fs * qs;  // 3 E(|t|)
            rs.resize(rs.deg() + 1);
            return qs.at(k) + rs.divAt(fs, k);
        }
        int h = 0, m = 1;
        for (; m < fs.size(); ++h, m <<= 1)
        {
        }
        if (k < m)
        {
            const Poly gs = fs.inv(k + 1); // 10 E(|f|)
            Mint sum;
            for (int i = 0, i0 = min<int>(k + 1, size()); i < i0; ++i)
                sum += (*this)[i] * gs[k - i];
            return sum;
        }
        assert(m << 1 <= LIM_POLY);
        polyWork0[0] = Mint(2U).inv();
        for (int hh = 0; hh < h; ++hh)
            for (int i = 0; i < 1 << hh; ++i)
                polyWork0[1 << hh | i] = polyWork0[i] * INV_FFT_ROOTS[hh + 2];
        const Mint a = FFT_ROOTS[h + 1];
        memcpy(polyWork2, data(), size() * sizeof(Mint));
        memset(polyWork2 + size(), 0, ((m << 1) - size()) * sizeof(Mint));
        fft(polyWork2, m << 1); // 2 E(|f|)
        memcpy(polyWork1, fs.data(), fs.size() * sizeof(Mint));
        memset(polyWork1 + fs.size(), 0, ((m << 1) - fs.size()) * sizeof(Mint));
        fft(polyWork1, m << 1); // 2 E(|f|)
        for (;;)
        {
            if (k & 1)
            {
                for (int i = 0; i < m; ++i)
                    polyWork2[i] = polyWork0[i] * (polyWork2[i << 1 | 0] * polyWork1[i << 1 | 1] - polyWork2[i << 1 | 1] * polyWork1[i << 1 | 0]);
            }
            else
            {
                for (int i = 0; i < m; ++i)
                {
                    polyWork2[i] = polyWork2[i << 1 | 0] * polyWork1[i << 1 | 1] + polyWork2[i << 1 | 1] * polyWork1[i << 1 | 0];
                    polyWork2[i].x = ((polyWork2[i].x & 1) ? (polyWork2[i].x + MO) : polyWork2[i].x) >> 1;
                }
            }
            for (int i = 0; i < m; ++i)
                polyWork1[i] = polyWork1[i << 1 | 0] * polyWork1[i << 1 | 1];
            if ((k >>= 1) < m)
            {
                invFft(polyWork2, m); // 1 E(|f|)
                invFft(polyWork1, m); // 1 E(|f|)
                // Poly::inv does not use polyWork2
                const Poly gs = Poly(vector<Mint>(polyWork1, polyWork1 + k + 1)).inv(k + 1); // 10 E(|f|)
                Mint sum;
                for (int i = 0; i <= k; ++i)
                    sum += polyWork2[i] * gs[k - i];
                return sum;
            }
            memcpy(polyWork2 + m, polyWork2, m * sizeof(Mint));
            invFft(polyWork2 + m, m); // (floor(log_2 k) - ceil(log_2 |f|)) E(|f|)
            memcpy(polyWork1 + m, polyWork1, m * sizeof(Mint));
            invFft(polyWork1 + m, m); // (floor(log_2 k) - ceil(log_2 |f|)) E(|f|)
            Mint aa = 1;
            for (int i = m; i < m << 1; ++i)
            {
                polyWork2[i] *= aa;
                polyWork1[i] *= aa;
                aa *= a;
            }
            fft(polyWork2 + m, m); // (floor(log_2 k) - ceil(log_2 |f|)) E(|f|)
            fft(polyWork1 + m, m); // (floor(log_2 k) - ceil(log_2 |f|)) E(|f|)
        }
    }
    // 13 E(n)
    // D log(t) = (D t) / t
    Poly log(int n) const
    {
        assert(!empty());
        assert((*this)[0].x == 1U);
        assert(n <= LIM_INV);
        Poly fs = mod(n);
        for (int i = 0; i < fs.size(); ++i)
            fs[i] *= i;
        fs = fs.div(*this, n);
        for (int i = 1; i < n; ++i)
            fs[i] *= ::inv[i];
        return fs;
    }
    // (16 + 1/2) E(n)
    // f = exp(t) mod x^m  ==>  (D f) / f == D t  (mod x^m)
    // g = (1 / exp(t)) mod x^m
    // f <- f - (log f - t) / (1 / f)
    //   =  f - (I ((D f) / f) - t) f
    //   == f - (I ((D f) / f + (f g - 1) ((D f) / f - D (t mod x^m))) - t) f  (mod x^(2m))
    //   =  f - (I (g (D f - f D (t mod x^m)) + D (t mod x^m)) - t) f
    // g <- g - (f g - 1) g
    // polyWork1: DFT(f, 2 m), polyWork2: g, polyWork3: DFT(g, 2 m)
    Poly exp(int n) const
    {
        assert(!empty());
        assert(!(*this)[0]);
        assert(1 <= n);
        assert(n == 1 || 1 << (32 - __builtin_clz(n - 1)) <= min(LIM_INV, LIM_POLY));
        if (n == 1)
            return {1U};
        if (n == 2)
            return {1U, at(1)};
        Poly fs(n);
        fs[0].x = polyWork1[0].x = polyWork1[1].x = polyWork2[0].x = 1U;
        int m;
        for (m = 1; m << 1 < n; m <<= 1)
        {
            for (int i = 0, i0 = min(m, size()); i < i0; ++i)
                polyWork0[i] = i * (*this)[i];
            memset(polyWork0 + min(m, size()), 0, (m - min(m, size())) * sizeof(Mint));
            fft(polyWork0, m); // (1/2) E(n)
            for (int i = 0; i < m; ++i)
                polyWork0[i] *= polyWork1[i];
            invFft(polyWork0, m); // (1/2) E(n)
            for (int i = 0; i < m; ++i)
                polyWork0[i] -= i * fs[i];
            memset(polyWork0 + m, 0, m * sizeof(Mint));
            fft(polyWork0, m << 1); // 1 E(n)
            memcpy(polyWork3, polyWork2, m * sizeof(Mint));
            memset(polyWork3 + m, 0, m * sizeof(Mint));
            fft(polyWork3, m << 1); // 1 E(n)
            for (int i = 0; i < m << 1; ++i)
                polyWork0[i] *= polyWork3[i];
            invFft(polyWork0, m << 1); // 1 E(n)
            for (int i = 0; i < m; ++i)
                polyWork0[i] *= ::inv[m + i];
            for (int i = 0, i0 = min(m, size() - m); i < i0; ++i)
                polyWork0[i] += (*this)[m + i];
            memset(polyWork0 + m, 0, m * sizeof(Mint));
            fft(polyWork0, m << 1); // 1 E(n)
            for (int i = 0; i < m << 1; ++i)
                polyWork0[i] *= polyWork1[i];
            invFft(polyWork0, m << 1); // 1 E(n)
            memcpy(fs.data() + m, polyWork0, m * sizeof(Mint));
            memcpy(polyWork1, fs.data(), (m << 1) * sizeof(Mint));
            memset(polyWork1 + (m << 1), 0, (m << 1) * sizeof(Mint));
            fft(polyWork1, m << 2); // 2 E(n)
            for (int i = 0; i < m << 1; ++i)
                polyWork0[i] = polyWork1[i] * polyWork3[i];
            invFft(polyWork0, m << 1); // 1 E(n)
            memset(polyWork0, 0, m * sizeof(Mint));
            fft(polyWork0, m << 1); // 1 E(n)
            for (int i = 0; i < m << 1; ++i)
                polyWork0[i] *= polyWork3[i];
            invFft(polyWork0, m << 1); // 1 E(n)
            for (int i = m; i < m << 1; ++i)
                polyWork2[i] = -polyWork0[i];
        }
        for (int i = 0, i0 = min(m, size()); i < i0; ++i)
            polyWork0[i] = i * (*this)[i];
        memset(polyWork0 + min(m, size()), 0, (m - min(m, size())) * sizeof(Mint));
        fft(polyWork0, m); // (1/2) E(n)
        for (int i = 0; i < m; ++i)
            polyWork0[i] *= polyWork1[i];
        invFft(polyWork0, m); // (1/2) E(n)
        for (int i = 0; i < m; ++i)
            polyWork0[i] -= i * fs[i];
        memcpy(polyWork0 + m, polyWork0 + (m >> 1), (m >> 1) * sizeof(Mint));
        memset(polyWork0 + (m >> 1), 0, (m >> 1) * sizeof(Mint));
        memset(polyWork0 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));
        fft(polyWork0, m);     // (1/2) E(n)
        fft(polyWork0 + m, m); // (1/2) E(n)
        memcpy(polyWork3 + m, polyWork2 + (m >> 1), (m >> 1) * sizeof(Mint));
        memset(polyWork3 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));
        fft(polyWork3 + m, m); // (1/2) E(n)
        for (int i = 0; i < m; ++i)
            polyWork0[m + i] = polyWork0[i] * polyWork3[m + i] + polyWork0[m + i] * polyWork3[i];
        for (int i = 0; i < m; ++i)
            polyWork0[i] *= polyWork3[i];
        invFft(polyWork0, m);     // (1/2) E(n)
        invFft(polyWork0 + m, m); // (1/2) E(n)
        for (int i = 0; i < m >> 1; ++i)
            polyWork0[(m >> 1) + i] += polyWork0[m + i];
        for (int i = 0; i < m; ++i)
            polyWork0[i] *= ::inv[m + i];
        for (int i = 0, i0 = min(m, size() - m); i < i0; ++i)
            polyWork0[i] += (*this)[m + i];
        memset(polyWork0 + m, 0, m * sizeof(Mint));
        fft(polyWork0, m << 1); // 1 E(n)
        for (int i = 0; i < m << 1; ++i)
            polyWork0[i] *= polyWork1[i];
        invFft(polyWork0, m << 1); // 1 E(n)
        memcpy(fs.data() + m, polyWork0, (n - m) * sizeof(Mint));
        return fs;
    }
    // (29 + 1/2) E(n)
    // g <- g - (log g - a log t) g
    Poly pow(Mint a, int n) const
    {
        assert(!empty());
        assert((*this)[0].x == 1U);
        assert(1 <= n);
        return (a * log(n)).exp(n); // 13 E(n) + (16 + 1/2) E(n)
    }
    // (29 + 1/2) E(n - a ord(t))
    Poly pow(long long a, int n) const
    {
        assert(a >= 0);
        assert(1 <= n);
        if (a == 0)
        {
            Poly gs(n);
            gs[0].x = 1U;
            return gs;
        }
        const int o = ord();
        if (o == -1 || o > (n - 1) / a)
            return Poly(n);
        const Mint b = (*this)[o].inv(), c = (*this)[o].pow(a);
        const int ntt = min<int>(n - a * o, size() - o);
        Poly tts(ntt);
        for (int i = 0; i < ntt; ++i)
            tts[i] = b * (*this)[o + i];
        tts = tts.pow(Mint(a), n - a * o); // (29 + 1/2) E(n - a ord(t))
        Poly gs(n);
        for (int i = 0; i < n - a * o; ++i)
            gs[a * o + i] = c * tts[i];
        return gs;
    }
    // (10 + 1/2) E(n)
    // f = t^(1/2) mod x^m,  g = 1 / t^(1/2) mod x^m
    // f <- f - (f^2 - h) g / 2
    // g <- g - (f g - 1) g
    // polyWork1: DFT(f, m), polyWork2: g, polyWork3: DFT(g, 2 m)
    Poly sqrt(int n) const
    {
        assert(!empty());
        assert((*this)[0].x == 1U);
        assert(1 <= n);
        assert(n == 1 || 1 << (32 - __builtin_clz(n - 1)) <= LIM_POLY);
        if (n == 1)
            return {1U};
        if (n == 2)
            return {1U, at(1) / 2};
        Poly fs(n);
        fs[0].x = polyWork1[0].x = polyWork2[0].x = 1U;
        int m;
        for (m = 1; m << 1 < n; m <<= 1)
        {
            for (int i = 0; i < m; ++i)
                polyWork1[i] *= polyWork1[i];
            invFft(polyWork1, m); // (1/2) E(n)
            for (int i = 0, i0 = min(m, size()); i < i0; ++i)
                polyWork1[i] -= (*this)[i];
            for (int i = 0, i0 = min(m, size() - m); i < i0; ++i)
                polyWork1[i] -= (*this)[m + i];
            memset(polyWork1 + m, 0, m * sizeof(Mint));
            fft(polyWork1, m << 1); // 1 E(n)
            memcpy(polyWork3, polyWork2, m * sizeof(Mint));
            memset(polyWork3 + m, 0, m * sizeof(Mint));
            fft(polyWork3, m << 1); // 1 E(n)
            for (int i = 0; i < m << 1; ++i)
                polyWork1[i] *= polyWork3[i];
            invFft(polyWork1, m << 1); // 1 E(n)
            for (int i = 0; i < m; ++i)
            {
                polyWork1[i] = -polyWork1[i];
                fs[m + i].x = ((polyWork1[i].x & 1) ? (polyWork1[i].x + MO) : polyWork1[i].x) >> 1;
            }
            memcpy(polyWork1, fs.data(), (m << 1) * sizeof(Mint));
            fft(polyWork1, m << 1); // 1 E(n)
            for (int i = 0; i < m << 1; ++i)
                polyWork0[i] = polyWork1[i] * polyWork3[i];
            invFft(polyWork0, m << 1); // 1 E(n)
            memset(polyWork0, 0, m * sizeof(Mint));
            fft(polyWork0, m << 1); // 1 E(n)
            for (int i = 0; i < m << 1; ++i)
                polyWork0[i] *= polyWork3[i];
            invFft(polyWork0, m << 1); // 1 E(n)
            for (int i = m; i < m << 1; ++i)
                polyWork2[i] = -polyWork0[i];
        }
        for (int i = 0; i < m; ++i)
            polyWork1[i] *= polyWork1[i];
        invFft(polyWork1, m); // (1/2) E(n)
        for (int i = 0, i0 = min(m, size()); i < i0; ++i)
            polyWork1[i] -= (*this)[i];
        for (int i = 0, i0 = min(m, size() - m); i < i0; ++i)
            polyWork1[i] -= (*this)[m + i];
        memcpy(polyWork1 + m, polyWork1 + (m >> 1), (m >> 1) * sizeof(Mint));
        memset(polyWork1 + (m >> 1), 0, (m >> 1) * sizeof(Mint));
        memset(polyWork1 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));
        fft(polyWork1, m);     // (1/2) E(n)
        fft(polyWork1 + m, m); // (1/2) E(n)
        memcpy(polyWork3 + m, polyWork2 + (m >> 1), (m >> 1) * sizeof(Mint));
        memset(polyWork3 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));
        fft(polyWork3 + m, m); // (1/2) E(n)
        // for (int i = 0; i < m << 1; ++i) polyWork1[i] *= polyWork3[i];
        for (int i = 0; i < m; ++i)
            polyWork1[m + i] = polyWork1[i] * polyWork3[m + i] + polyWork1[m + i] * polyWork3[i];
        for (int i = 0; i < m; ++i)
            polyWork1[i] *= polyWork3[i];
        invFft(polyWork1, m);     // (1/2) E(n)
        invFft(polyWork1 + m, m); // (1/2) E(n)
        for (int i = 0; i < m >> 1; ++i)
            polyWork1[(m >> 1) + i] += polyWork1[m + i];
        for (int i = 0; i < n - m; ++i)
        {
            polyWork1[i] = -polyWork1[i];
            fs[m + i].x = ((polyWork1[i].x & 1) ? (polyWork1[i].x + MO) : polyWork1[i].x) >> 1;
        }
        return fs;
    }
    // (10 + 1/2) E(n)
    // modSqrt must return a quadratic residue if exists, or anything otherwise.
    // Return {} if *this does not have a square root.
    template <class F>
    Poly sqrt(int n, F modSqrt) const
    {
        assert(1 <= n);
        const int o = ord();
        if (o == -1)
            return Poly(n);
        if (o & 1)
            return {};
        const Mint c = modSqrt((*this)[o]);
        if (c * c != (*this)[o])
            return {};
        if (o >> 1 >= n)
            return Poly(n);
        const Mint b = (*this)[o].inv();
        const int ntt = min(n - (o >> 1), size() - o);
        Poly tts(ntt);
        for (int i = 0; i < ntt; ++i)
            tts[i] = b * (*this)[o + i];
        tts = tts.sqrt(n - (o >> 1)); // (10 + 1/2) E(n)
        Poly gs(n);
        for (int i = 0; i < n - (o >> 1); ++i)
            gs[(o >> 1) + i] = c * tts[i];
        return gs;
    }
    // 6 E(|t|)
    // x -> x + a
    Poly shift(const Mint &a) const
    {
        if (empty())
            return {};
        const int n = size();
        int m = 1;
        for (; m < n; m <<= 1)
        {
        }
        for (int i = 0; i < n; ++i)
            polyWork0[i] = fac[i] * (*this)[i];
        memset(polyWork0 + n, 0, ((m << 1) - n) * sizeof(Mint));
        fft(polyWork0, m << 1); // 2 E(|t|)
        {
            Mint aa = 1;
            for (int i = 0; i < n; ++i)
            {
                polyWork1[n - 1 - i] = invFac[i] * aa;
                aa *= a;
            }
        }
        memset(polyWork1 + n, 0, ((m << 1) - n) * sizeof(Mint));
        fft(polyWork1, m << 1); // 2 E(|t|)
        for (int i = 0; i < m << 1; ++i)
            polyWork0[i] *= polyWork1[i];
        invFft(polyWork0, m << 1); // 2 E(|t|)
        Poly fs(n);
        for (int i = 0; i < n; ++i)
            fs[i] = invFac[i] * polyWork0[n - 1 + i];
        return fs;
    }
};

Mint linearRecurrenceAt(const vector<Mint> &as, const vector<Mint> &cs, long long k)
{
    assert(!cs.empty());
    assert(cs[0]);
    const int d = cs.size() - 1;
    assert(as.size() >= static_cast<size_t>(d));
    return (Poly(vector<Mint>(as.begin(), as.begin() + d)) * cs).mod(d).divAt(cs, k);
}

struct SubproductTree
{
    int logN, n, nn;
    vector<Mint> xs;
    // [DFT_4((X-xs[0])(X-xs[1])(X-xs[2])(X-xs[3]))] [(X-xs[0])(X-xs[1])(X-xs[2])(X-xs[3])mod X^4]
    // [         DFT_4((X-xs[0])(X-xs[1]))         ] [         DFT_4((X-xs[2])(X-xs[3]))         ]
    // [   DFT_2(X-xs[0])   ] [   DFT_2(X-xs[1])   ] [   DFT_2(X-xs[2])   ] [   DFT_2(X-xs[3])   ]
    vector<Mint> buf;
    vector<Mint *> gss;
    // (1 - xs[0] X) ... (1 - xs[nn-1] X)
    Poly all;
    // (ceil(log_2 n) + O(1)) E(n)
    SubproductTree(const vector<Mint> &xs_)
    {
        n = xs_.size();
        for (logN = 0, nn = 1; nn < n; ++logN, nn <<= 1)
        {
        }
        xs.assign(nn, 0U);
        memcpy(xs.data(), xs_.data(), n * sizeof(Mint));
        buf.assign((logN + 1) * (nn << 1), 0U);
        gss.assign(nn << 1, nullptr);
        for (int h = 0; h <= logN; ++h)
            for (int u = 1 << h; u < 1 << (h + 1); ++u)
            {
                gss[u] = buf.data() + (h * (nn << 1) + ((u - (1 << h)) << (logN - h + 1)));
            }
        for (int i = 0; i < nn; ++i)
        {
            gss[nn + i][0] = -xs[i] + 1;
            gss[nn + i][1] = -xs[i] - 1;
        }
        if (nn == 1)
            gss[1][1] += 2;
        for (int h = logN; --h >= 0;)
        {
            const int m = 1 << (logN - h);
            for (int u = 1 << (h + 1); --u >= 1 << h;)
            {
                for (int i = 0; i < m; ++i)
                    gss[u][i] = gss[u << 1][i] * gss[u << 1 | 1][i];
                memcpy(gss[u] + m, gss[u], m * sizeof(Mint));
                invFft(gss[u] + m, m); // ((1/2) ceil(log_2 n) + O(1)) E(n)
                if (h > 0)
                {
                    gss[u][m] -= 2;
                    const Mint a = FFT_ROOTS[logN - h + 1];
                    Mint aa = 1;
                    for (int i = m; i < m << 1; ++i)
                    {
                        gss[u][i] *= aa;
                        aa *= a;
                    };
                    fft(gss[u] + m, m); // ((1/2) ceil(log_2 n) + O(1)) E(n)
                }
            }
        }
        all.resize(nn + 1);
        all[0] = 1;
        for (int i = 1; i < nn; ++i)
            all[i] = gss[1][nn + nn - i];
        all[nn] = gss[1][nn] - 1;
    }
    // ((3/2) ceil(log_2 n) + O(1)) E(n) + 10 E(|f|) + 3 E(|f| + 2^(ceil(log_2 n)))
    vector<Mint> multiEval(const Poly &fs) const
    {
        vector<Mint> work0(nn), work1(nn), work2(nn);
        {
            const int m = max(fs.size(), 1);
            auto invAll = all.inv(m); // 10 E(|f|)
            std::reverse(invAll.begin(), invAll.end());
            int mm;
            for (mm = 1; mm < m - 1 + nn; mm <<= 1)
            {
            }
            invAll.resize(mm, 0U);
            fft(invAll); // E(|f| + 2^(ceil(log_2 n)))
            vector<Mint> ffs(mm, 0U);
            memcpy(ffs.data(), fs.data(), fs.size() * sizeof(Mint));
            fft(ffs); // E(|f| + 2^(ceil(log_2 n)))
            for (int i = 0; i < mm; ++i)
                ffs[i] *= invAll[i];
            invFft(ffs); // E(|f| + 2^(ceil(log_2 n)))
            memcpy(((logN & 1) ? work1 : work0).data(), ffs.data() + m - 1, nn * sizeof(Mint));
        }
        for (int h = 0; h < logN; ++h)
        {
            const int m = 1 << (logN - h);
            for (int u = 1 << h; u < 1 << (h + 1); ++u)
            {
                Mint *hs = (((logN - h) & 1) ? work1 : work0).data() + ((u - (1 << h)) << (logN - h));
                Mint *hs0 = (((logN - h) & 1) ? work0 : work1).data() + ((u - (1 << h)) << (logN - h));
                Mint *hs1 = hs0 + (m >> 1);
                fft(hs, m); // ((1/2) ceil(log_2 n) + O(1)) E(n)
                for (int i = 0; i < m; ++i)
                    work2[i] = gss[u << 1 | 1][i] * hs[i];
                invFft(work2.data(), m); // ((1/2) ceil(log_2 n) + O(1)) E(n)
                memcpy(hs0, work2.data() + (m >> 1), (m >> 1) * sizeof(Mint));
                for (int i = 0; i < m; ++i)
                    work2[i] = gss[u << 1][i] * hs[i];
                invFft(work2.data(), m); // ((1/2) ceil(log_2 n) + O(1)) E(n)
                memcpy(hs1, work2.data() + (m >> 1), (m >> 1) * sizeof(Mint));
            }
        }
        work0.resize(n);
        return work0;
    }
    // ((5/2) ceil(log_2 n) + O(1)) E(n)
    Poly interpolate(const vector<Mint> &ys) const
    {
        assert(static_cast<int>(ys.size()) == n);
        Poly gs(n);
        for (int i = 0; i < n; ++i)
            gs[i] = (i + 1) * all[n - (i + 1)];
        const vector<Mint> denoms = multiEval(gs); // ((3/2) ceil(log_2 n) + O(1)) E(n)
        vector<Mint> work(nn << 1, 0U);
        for (int i = 0; i < n; ++i)
        {
            // xs[0], ..., xs[n - 1] are not distinct
            assert(denoms[i]);
            work[i << 1] = work[i << 1 | 1] = ys[i] / denoms[i];
        }
        for (int h = logN; --h >= 0;)
        {
            const int m = 1 << (logN - h);
            for (int u = 1 << (h + 1); --u >= 1 << h;)
            {
                Mint *hs = work.data() + ((u - (1 << h)) << (logN - h + 1));
                for (int i = 0; i < m; ++i)
                    hs[i] = gss[u << 1 | 1][i] * hs[i] + gss[u << 1][i] * hs[m + i];
                if (h > 0)
                {
                    memcpy(hs + m, hs, m * sizeof(Mint));
                    invFft(hs + m, m); // ((1/2) ceil(log_2 n) + O(1)) E(n)
                    const Mint a = FFT_ROOTS[logN - h + 1];
                    Mint aa = 1;
                    for (int i = m; i < m << 1; ++i)
                    {
                        hs[i] *= aa;
                        aa *= a;
                    };
                    fft(hs + m, m); // ((1/2) ceil(log_2 n) + O(1)) E(n)
                }
            }
        }
        invFft(work.data(), nn); // E(n)
        return Poly(vector<Mint>(work.data() + nn - n, work.data() + nn));
    }
};
int main()
{
    int n = FastIO::rd() +1, m = FastIO::rd() + 1;
    vector<Mint> a(n), b(m);
    for (int i = 0; i < n; ++i)
        a[i].x = FastIO::rd();
    for (int i = 0; i < m; ++i)
        b[i].x = FastIO::rd();
    vector<Mint> res = convolve(a, b);
    for (int i = 0; i < n + m - 1; ++i)
        FastIO::wt(res[i].x, (i == n + m - 2) ? '\n' : ' ');
}

詳細信息

answer.code:4:10: fatal error: algorithm: No such file or directory
 #include <algorithm>
          ^~~~~~~~~~~
compilation terminated.