結果

問題 No.2583 Differential Equation (Enhanced version)
ユーザー noshi91noshi91
提出日時 2023-12-11 02:37:02
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 766 ms / 10,000 ms
コード長 22,689 bytes
コンパイル時間 3,100 ms
コンパイル使用メモリ 232,080 KB
実行使用メモリ 20,268 KB
最終ジャッジ日時 2024-09-27 04:16:42
合計ジャッジ時間 13,679 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
（要ログイン）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 2 ms
6,816 KB
testcase_03 AC 5 ms
6,944 KB
testcase_04 AC 3 ms
6,940 KB
testcase_05 AC 5 ms
6,940 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 4 ms
6,940 KB
testcase_08 AC 4 ms
6,940 KB
testcase_09 AC 6 ms
6,940 KB
testcase_10 AC 4 ms
6,940 KB
testcase_11 AC 6 ms
6,944 KB
testcase_12 AC 3 ms
6,944 KB
testcase_13 AC 356 ms
11,952 KB
testcase_14 AC 81 ms
6,940 KB
testcase_15 AC 177 ms
7,060 KB
testcase_16 AC 732 ms
16,876 KB
testcase_17 AC 46 ms
6,944 KB
testcase_18 AC 356 ms
10,288 KB
testcase_19 AC 184 ms
8,152 KB
testcase_20 AC 176 ms
7,152 KB
testcase_21 AC 10 ms
6,940 KB
testcase_22 AC 380 ms
13,144 KB
testcase_23 AC 753 ms
19,760 KB
testcase_24 AC 766 ms
19,740 KB
testcase_25 AC 759 ms
19,760 KB
testcase_26 AC 766 ms
19,752 KB
testcase_27 AC 760 ms
19,884 KB
testcase_28 AC 168 ms
6,944 KB
testcase_29 AC 751 ms
18,652 KB
testcase_30 AC 87 ms
6,944 KB
testcase_31 AC 5 ms
6,944 KB
testcase_32 AC 5 ms
6,940 KB
testcase_33 AC 4 ms
6,944 KB
testcase_34 AC 2 ms
6,944 KB
testcase_35 AC 14 ms
6,944 KB
testcase_36 AC 2 ms
6,940 KB
testcase_37 AC 14 ms
6,940 KB
testcase_38 AC 751 ms
20,268 KB
testcase_39 AC 758 ms
19,756 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

// https://ei1333.github.io/library/test/verify/yosupo-exp-of-formal-power-series.test.cpp

// #line 1 "test/verify/yosupo-exp-of-formal-power-series.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/exp_of_formal_power_series"

// #line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v)
    is >> in;
  return is;
}

template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64> vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t)
    fill_v(e, v);
}

template <typename F> struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args> decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F> inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
// #line 4 "test/verify/yosupo-exp-of-formal-power-series.test.cpp"

// #line 1 "math/combinatorics/mod-int.hpp"
template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt<mod>;
// #line 6 "test/verify/yosupo-exp-of-formal-power-series.test.cpp"

// #line 2 "math/fps/formal-power-series-friendly-ntt.hpp"

// #line 1 "math/fft/number-theoretic-transform-friendly-mod-int.hpp"
/**
 * @brief Number Theoretic Transform Friendly ModInt
 */
template <typename Mint> struct NumberTheoreticTransformFriendlyModInt {

  static vector<Mint> roots, iroots, rate3, irate3;
  static int max_base;

  NumberTheoreticTransformFriendlyModInt() = default;

  static void init() {
    if (roots.empty()) {
      const unsigned mod = Mint::get_mod();
      assert(mod >= 3 && mod % 2 == 1);
      auto tmp = mod - 1;
      max_base = 0;
      while (tmp % 2 == 0)
        tmp >>= 1, max_base++;
      Mint root = 2;
      while (root.pow((mod - 1) >> 1) == 1) {
        root += 1;
      }
      assert(root.pow(mod - 1) == 1);

      roots.resize(max_base + 1);
      iroots.resize(max_base + 1);
      rate3.resize(max_base + 1);
      irate3.resize(max_base + 1);

      roots[max_base] = root.pow((mod - 1) >> max_base);
      iroots[max_base] = Mint(1) / roots[max_base];
      for (int i = max_base - 1; i >= 0; i--) {
        roots[i] = roots[i + 1] * roots[i + 1];
        iroots[i] = iroots[i + 1] * iroots[i + 1];
      }
      {
        Mint prod = 1, iprod = 1;
        for (int i = 0; i <= max_base - 3; i++) {
          rate3[i] = roots[i + 3] * prod;
          irate3[i] = iroots[i + 3] * iprod;
          prod *= iroots[i + 3];
          iprod *= roots[i + 3];
        }
      }
    }
  }

  static void ntt(vector<Mint> &a) {
    init();
    const int n = (int)a.size();
    assert((n & (n - 1)) == 0);
    int h = __builtin_ctz(n);
    assert(h <= max_base);
    int len = 0;
    Mint imag = roots[2];
    if (h & 1) {
      int p = 1 << (h - 1);
      Mint rot = 1;
      for (int i = 0; i < p; i++) {
        auto r = a[i + p];
        a[i + p] = a[i] - r;
        a[i] += r;
      }
      len++;
    }
    for (; len + 1 < h; len += 2) {
      int p = 1 << (h - len - 2);
      { // s = 0
        for (int i = 0; i < p; i++) {
          auto a0 = a[i];
          auto a1 = a[i + p];
          auto a2 = a[i + 2 * p];
          auto a3 = a[i + 3 * p];
          auto a1na3imag = (a1 - a3) * imag;
          auto a0a2 = a0 + a2;
          auto a1a3 = a1 + a3;
          auto a0na2 = a0 - a2;
          a[i] = a0a2 + a1a3;
          a[i + 1 * p] = a0a2 - a1a3;
          a[i + 2 * p] = a0na2 + a1na3imag;
          a[i + 3 * p] = a0na2 - a1na3imag;
        }
      }
      Mint rot = rate3[0];
      for (int s = 1; s < (1 << len); s++) {
        int offset = s << (h - len);
        Mint rot2 = rot * rot;
        Mint rot3 = rot2 * rot;
        for (int i = 0; i < p; i++) {
          auto a0 = a[i + offset];
          auto a1 = a[i + offset + p] * rot;
          auto a2 = a[i + offset + 2 * p] * rot2;
          auto a3 = a[i + offset + 3 * p] * rot3;
          auto a1na3imag = (a1 - a3) * imag;
          auto a0a2 = a0 + a2;
          auto a1a3 = a1 + a3;
          auto a0na2 = a0 - a2;
          a[i + offset] = a0a2 + a1a3;
          a[i + offset + 1 * p] = a0a2 - a1a3;
          a[i + offset + 2 * p] = a0na2 + a1na3imag;
          a[i + offset + 3 * p] = a0na2 - a1na3imag;
        }
        rot *= rate3[__builtin_ctz(~s)];
      }
    }
  }

  static void intt(vector<Mint> &a, bool f = true) {
    init();
    const int n = (int)a.size();
    assert((n & (n - 1)) == 0);
    int h = __builtin_ctz(n);
    assert(h <= max_base);
    int len = h;
    Mint iimag = iroots[2];
    for (; len > 1; len -= 2) {
      int p = 1 << (h - len);
      { // s = 0
        for (int i = 0; i < p; i++) {
          auto a0 = a[i];
          auto a1 = a[i + 1 * p];
          auto a2 = a[i + 2 * p];
          auto a3 = a[i + 3 * p];
          auto a2na3iimag = (a2 - a3) * iimag;
          auto a0na1 = a0 - a1;
          auto a0a1 = a0 + a1;
          auto a2a3 = a2 + a3;
          a[i] = a0a1 + a2a3;
          a[i + 1 * p] = (a0na1 + a2na3iimag);
          a[i + 2 * p] = (a0a1 - a2a3);
          a[i + 3 * p] = (a0na1 - a2na3iimag);
        }
      }
      Mint irot = irate3[0];
      for (int s = 1; s < (1 << (len - 2)); s++) {
        int offset = s << (h - len + 2);
        Mint irot2 = irot * irot;
        Mint irot3 = irot2 * irot;
        for (int i = 0; i < p; i++) {
          auto a0 = a[i + offset];
          auto a1 = a[i + offset + 1 * p];
          auto a2 = a[i + offset + 2 * p];
          auto a3 = a[i + offset + 3 * p];
          auto a2na3iimag = (a2 - a3) * iimag;
          auto a0na1 = a0 - a1;
          auto a0a1 = a0 + a1;
          auto a2a3 = a2 + a3;
          a[i + offset] = a0a1 + a2a3;
          a[i + offset + 1 * p] = (a0na1 + a2na3iimag) * irot;
          a[i + offset + 2 * p] = (a0a1 - a2a3) * irot2;
          a[i + offset + 3 * p] = (a0na1 - a2na3iimag) * irot3;
        }
        irot *= irate3[__builtin_ctz(~s)];
      }
    }
    if (len >= 1) {
      int p = 1 << (h - 1);
      for (int i = 0; i < p; i++) {
        auto ajp = a[i] - a[i + p];
        a[i] += a[i + p];
        a[i + p] = ajp;
      }
    }
    if (f) {
      Mint inv_sz = Mint(1) / n;
      for (int i = 0; i < n; i++)
        a[i] *= inv_sz;
    }
  }

  static vector<Mint> multiply(vector<Mint> a, vector<Mint> b) {
    int need = a.size() + b.size() - 1;
    int nbase = 1;
    while ((1 << nbase) < need)
      nbase++;
    int sz = 1 << nbase;
    a.resize(sz, 0);
    b.resize(sz, 0);
    ntt(a);
    ntt(b);
    Mint inv_sz = Mint(1) / sz;
    for (int i = 0; i < sz; i++)
      a[i] *= b[i] * inv_sz;
    intt(a, false);
    a.resize(need);
    return a;
  }
};

template <typename Mint>
vector<Mint>
    NumberTheoreticTransformFriendlyModInt<Mint>::roots = vector<Mint>();
template <typename Mint>
vector<Mint>
    NumberTheoreticTransformFriendlyModInt<Mint>::iroots = vector<Mint>();
template <typename Mint>
vector<Mint>
    NumberTheoreticTransformFriendlyModInt<Mint>::rate3 = vector<Mint>();
template <typename Mint>
vector<Mint>
    NumberTheoreticTransformFriendlyModInt<Mint>::irate3 = vector<Mint>();
template <typename Mint>
int NumberTheoreticTransformFriendlyModInt<Mint>::max_base = 0;
// #line 4 "math/fps/formal-power-series-friendly-ntt.hpp"

template <typename T> struct FormalPowerSeriesFriendlyNTT : vector<T> {
  using vector<T>::vector;
  using P = FormalPowerSeriesFriendlyNTT;
  using NTT = NumberTheoreticTransformFriendlyModInt<T>;

  P pre(int deg) const {
    return P(begin(*this), begin(*this) + min((int)this->size(), deg));
  }

  P rev(int deg = -1) const {
    P ret(*this);
    if (deg != -1)
      ret.resize(deg, T(0));
    reverse(begin(ret), end(ret));
    return ret;
  }

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

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

  P operator+(const T &v) const { return P(*this) += v; }

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

  P operator-(const T &v) const { return P(*this) -= v; }

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

  P operator*(const T &v) const { return P(*this) *= v; }

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

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

  P &operator+=(const P &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;
  }

  P &operator-=(const P &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;
  }

  // https://judge.yosupo.jp/problem/convolution_mod
  P &operator*=(const P &r) {
    if (this->empty() || r.empty()) {
      this->clear();
      return *this;
    }
    auto ret = NTT::multiply(*this, r);
    return *this = {begin(ret), end(ret)};
  }

  P &operator/=(const P &r) {
    if (this->size() < r.size()) {
      this->clear();
      return *this;
    }
    int n = this->size() - r.size() + 1;
    return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
  }

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

  // https://judge.yosupo.jp/problem/division_of_polynomials
  pair<P, P> div_mod(const P &r) {
    P q = *this / r;
    P x = *this - q * r;
    x.shrink();
    return make_pair(q, x);
  }

  P operator-() const {
    P ret(this->size());
    for (int i = 0; i < (int)this->size(); i++)
      ret[i] = -(*this)[i];
    return ret;
  }

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

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

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

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

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

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

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

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

  P integral() const {
    const int n = (int)this->size();
    P ret(n + 1);
    ret[0] = T(0);
    for (int i = 0; i < n; i++)
      ret[i + 1] = (*this)[i] / T(i + 1);
    return ret;
  }

  // https://judge.yosupo.jp/problem/inv_of_formal_power_series
  // F(0) must not be 0
  P inv(int deg = -1) const {
    assert(((*this)[0]) != T(0));
    const int n = (int)this->size();
    if (deg == -1)
      deg = n;
    P res(deg);
    res[0] = {T(1) / (*this)[0]};
    for (int d = 1; d < deg; d <<= 1) {
      P f(2 * d), g(2 * d);
      for (int j = 0; j < min(n, 2 * d); j++)
        f[j] = (*this)[j];
      for (int j = 0; j < d; j++)
        g[j] = res[j];
      NTT::ntt(f);
      NTT::ntt(g);
      f = f.dot(g);
      NTT::intt(f);
      for (int j = 0; j < d; j++)
        f[j] = 0;
      NTT::ntt(f);
      for (int j = 0; j < 2 * d; j++)
        f[j] *= g[j];
      NTT::intt(f);
      for (int j = d; j < min(2 * d, deg); j++)
        res[j] = -f[j];
    }
    return res;
  }

  // https://judge.yosupo.jp/problem/log_of_formal_power_series
  // F(0) must be 1
  P log(int deg = -1) const {
    assert((*this)[0] == T(1));
    const int n = (int)this->size();
    if (deg == -1)
      deg = n;
    return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
  }

  // https://judge.yosupo.jp/problem/sqrt_of_formal_power_series
  P sqrt(int deg = -1,
         const function<T(T)> &get_sqrt = [](T) { return T(1); }) const {
    const int n = (int)this->size();
    if (deg == -1)
      deg = n;
    if ((*this)[0] == T(0)) {
      for (int i = 1; i < n; i++) {
        if ((*this)[i] != T(0)) {
          if (i & 1)
            return {};
          if (deg - i / 2 <= 0)
            break;
          auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt);
          if (ret.empty())
            return {};
          ret = ret << (i / 2);
          if ((int)ret.size() < deg)
            ret.resize(deg, T(0));
          return ret;
        }
      }
      return P(deg, 0);
    }
    auto sqr = T(get_sqrt((*this)[0]));
    if (sqr * sqr != (*this)[0])
      return {};
    P ret{sqr};
    T inv2 = T(1) / T(2);
    for (int i = 1; i < deg; i <<= 1) {
      ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
    }
    return ret.pre(deg);
  }

  P sqrt(const function<T(T)> &get_sqrt, int deg = -1) const {
    return sqrt(deg, get_sqrt);
  }

  // https://judge.yosupo.jp/problem/exp_of_formal_power_series
  // F(0) must be 0
  P exp(int deg = -1) const {
    if (deg == -1)
      deg = this->size();
    assert((*this)[0] == T(0));

    P inv;
    inv.reserve(deg + 1);
    inv.push_back(T(0));
    inv.push_back(T(1));

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

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

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

  // https://judge.yosupo.jp/problem/pow_of_formal_power_series
  P pow(int64_t k, int deg = -1) const {
    const int n = (int)this->size();
    if (deg == -1)
      deg = n;
    if (k == 0) {
      P ret(deg, T(0));
      ret[0] = T(1);
      return ret;
    }
    for (int i = 0; i < n; i++) {
      if (i * k > deg)
        return P(deg, T(0));
      if ((*this)[i] != T(0)) {
        T rev = T(1) / (*this)[i];
        P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));
        ret = (ret << (i * k)).pre(deg);
        if ((int)ret.size() < deg)
          ret.resize(deg, T(0));
        return ret;
      }
    }
    return *this;
  }

  P mod_pow(int64_t k, P g) const {
    P modinv = g.rev().inv();
    auto get_div = [&](P base) {
      if (base.size() < g.size()) {
        base.clear();
        return base;
      }
      int n = base.size() - g.size() + 1;
      return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);
    };
    P x(*this), ret{1};
    while (k > 0) {
      if (k & 1) {
        ret *= x;
        ret -= get_div(ret) * g;
        ret.shrink();
      }
      x *= x;
      x -= get_div(x) * g;
      x.shrink();
      k >>= 1;
    }
    return ret;
  }

  // https://judge.yosupo.jp/problem/polynomial_taylor_shift
  P taylor_shift(T c) const {
    int n = (int)this->size();
    vector<T> fact(n), rfact(n);
    fact[0] = rfact[0] = T(1);
    for (int i = 1; i < n; i++)
      fact[i] = fact[i - 1] * T(i);
    rfact[n - 1] = T(1) / fact[n - 1];
    for (int i = n - 1; i > 1; i--)
      rfact[i - 1] = rfact[i] * T(i);
    P p(*this);
    for (int i = 0; i < n; i++)
      p[i] *= fact[i];
    p = p.rev();
    P bs(n, T(1));
    for (int i = 1; i < n; i++)
      bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1];
    p = (p * bs).pre(n);
    p = p.rev();
    for (int i = 0; i < n; i++)
      p[i] *= rfact[i];
    return p;
  }
};

template <typename Mint> using FPS = FormalPowerSeriesFriendlyNTT<Mint>;
// #line 8 "test/verify/yosupo-exp-of-formal-power-series.test.cpp"

/**
 * @brief Enumeration(組み合わせ)
 */
template <typename T> struct Enumeration {
private:
  static vector<T> _fact, _finv, _inv;

  inline static void expand(size_t sz) {
    if (_fact.size() < sz + 1) {
      int pre_sz = max(1, (int)_fact.size());
      _fact.resize(sz + 1, T(1));
      _finv.resize(sz + 1, T(1));
      _inv.resize(sz + 1, T(1));
      for (int i = pre_sz; i <= (int)sz; i++) {
        _fact[i] = _fact[i - 1] * T(i);
      }
      _finv[sz] = T(1) / _fact[sz];
      for (int i = (int)sz - 1; i >= pre_sz; i--) {
        _finv[i] = _finv[i + 1] * T(i + 1);
      }
      for (int i = pre_sz; i <= (int)sz; i++) {
        _inv[i] = _finv[i] * _fact[i - 1];
      }
    }
  }

public:
  explicit Enumeration(size_t sz = 0) { expand(sz); }

  static inline T fact(int k) {
    expand(k);
    return _fact[k];
  }

  static inline T finv(int k) {
    expand(k);
    return _finv[k];
  }

  static inline T inv(int k) {
    expand(k);
    return _inv[k];
  }

  static T P(int n, int r) {
    if (r < 0 || n < r)
      return 0;
    return fact(n) * finv(n - r);
  }

  static T C(int p, int q) {
    if (q < 0 || p < q)
      return 0;
    return fact(p) * finv(q) * finv(p - q);
  }

  static T H(int n, int r) {
    if (n < 0 || r < 0)
      return 0;
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};

template <typename T> vector<T> Enumeration<T>::_fact = vector<T>();
template <typename T> vector<T> Enumeration<T>::_finv = vector<T>();
template <typename T> vector<T> Enumeration<T>::_inv = vector<T>();

const int MOD = 998244353;
using mint = ModInt<MOD>;
using enu = Enumeration<mint>;

int main() {
  int N, M;
  cin >> N >> M;
  const int D = 2 * N + 2;
  FPS<mint> A(M);
  cin >> A;
  A.resize(D - 1);
  for (int i = 2; i < A.size(); i++)
    A[i] += A[i - 2];
  A = A.integral().exp();

  FPS<mint> target = FPS<mint>{0, 1} * A.inv();
  target.resize(D);
  FPS<mint> B(D);
  for (int i = 0; i < D; i++) {
    B[i] = enu::C(D - 1, i);
  }
  target *= B;
  target.resize(D);

  target = target.taylor_shift(-1).rev().taylor_shift(mint(2).inverse());

  for (int i = 0; i < D; i++) {
    target[i] *= mint(i * 2).pow(N);
  }

  target = target.taylor_shift(mint(-2).inverse()).rev().taylor_shift(1);

  target *= B.inv();
  target.resize(D);

  FPS<mint> ans = target * A;
  ans.resize(N + 2);

  for (int i = 0; i < N + 2; i++) {
    cout << ans[i] << " \n"[i + 1 == N + 2];
  }

  return 0;
}
0