#745430 (C++17) No.1875 Flip Cards

• 問題: No.1875 Flip Cards
• ユーザー: ei1333333
• 提出日時: 2022-03-11 23:56:08
• 言語: C++17 (gcc 15.2.0 + boost 1.89.0)
• 結果: WA
• 実行時間: -
• コード長: 20,405 bytes
• コンパイル時間: 6,984 ms
• コンパイル使用メモリ: 389,236 KB
• 実行使用メモリ: 10,924 KB
• 最終ジャッジ日時: 2026-06-25 13:01:34
• 合計ジャッジ時間: 26,755 ms
• ジャッジサーバーID （参考情報）: judge1_0 / judge2_1

ファイルパターン	結果
sample	WA * 3
other	WA * 2 TLE * 1 -- * 4

コンパイルメッセージ

In file included from /home/linuxbrew/.linuxbrew/Cellar/gcc/15.2.0_1/include/c++/15/x86_64-pc-linux-gnu/bits/c++allocator.h:33,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc/15.2.0_1/include/c++/15/bits/allocator.h:46,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc/15.2.0_1/include/c++/15/string:45,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc/15.2.0_1/include/c++/15/bitset:54,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc/15.2.0_1/include/c++/15/x86_64-pc-linux-gnu/bits/stdc++.h:54,
                 from main.cpp:5:
In member function 'void std::__new_allocator<_Tp>::deallocate(_Tp*, size_type) [with _Tp = atcoder::static_modint<998244353>]',
    inlined from 'static void std::allocator_traits<std::allocator<_CharT> >::deallocate(allocator_type&, pointer, size_type) [with _Tp = atcoder::static_modint<998244353>]' at /home/linuxbrew/.linuxbrew/Cellar/gcc/15.2.0_1/include/c++/15/bits/alloc_traits.h:649:23,
    inlined from 'void std::_Vector_base<_Tp, _Alloc>::_M_deallocate(pointer, std::size_t) [with _Tp = atcoder::static_modint<998244353>; _Alloc = std::allocator<atcoder::static_modint<998244353> >]' at /home/linuxbrew/.linuxbrew/Cellar/gcc/15.2.0_1/include/c++/15/bits/stl_vector.h:396:19,
    inlined from 'std::vector<_Tp, _Alloc>::_Guard_alloc::~_Guard_alloc() [with _Tp = atcoder::static_modint<998244353>; _Alloc = std::allocator<atcoder::static_modint<998244353> >]' at /home/linuxbrew/.linuxbrew/Cellar/gcc/15.2.0_1/include/c++/15/bits/stl_vector.h:1883:27,
    inlined from 'void std::vector<_Tp, _Alloc>::_M_realloc_append(_Args&& ...) [with _Args = {atcoder::static_modint<998244353, 0>}; _Tp = atcoder::static_modint<998244353>; _Alloc = std::allocator<atcoder::static_modint<998244353> >]' at /home/linuxbrew/.linuxbrew/Cellar/gcc/15.2.0_1/include/c++/15/bits/vector.tcc:640:7,
    inlined from 'std::vector<_Tp, _Alloc>::reference std::vector<_Tp, _Alloc>::emplace_back(_Args&& ...) [with _Args = {atcoder::stat

ソースコード

#pragma GCC target ("avx,avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

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

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;
// const int mod = 998244353;

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 {
  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)};
}

using mint = atcoder::modint998244353;

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 <= 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 <= 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 >();

using E = Enumeration< mint >;

#line 1 "math/fft/number-theoretic-transform-friendly-mod-int.cpp"

/**
 * @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::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 2 "math/fps/formal-power-series-friendly-ntt.cpp"

/**
 * @brief Formal Power Series Friendly NTT(NTTmod用形式的冪級数)
 * @docs docs/formal-power-series-friendly-ntt.md
 */
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::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;
    for(int i = 0; i < n; i++) {
      if((*this)[i] != T(0)) {
        T rev = T(1) / (*this)[i];
        P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));
        if(i * k > deg) return P(deg, T(0));
        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 >;

int main() {
  int N, M;
  cin >> N >> M;
  mint all = 1;
  using fps = FPS< mint >;
  vector< fps > ue(N), sita(N);
  for(int i = 0; i < N; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    all *= mint(a).pow(c);
    auto t = mint(b) / a;
    ue[i] = fps{t * c};
    sita[i] = fps{1, t};
  }
  auto dp_ = MFP([&](auto rec, int l, int r) -> pair< fps, fps > {
    if(l + 1 >= r) return {ue[l], sita[l]};
    int m = (l + r) / 2;
    auto x = rec(l, m);
    auto y = rec(m, r);
    return {x.first * y.second + x.second * y.first, x.second * y.second};
  })(0, N);
  auto dp1 = dp_.first * dp_.second.inv(M + 1);
  dp1.resize(M + 1);
  dp1 = dp1.integral();
  dp1 = dp1.exp();
  vector< mint > dp{1};
  for(int k = 1; k <= M; k++) {
    vector< mint > dp2(k + 1);
    for(int i = 1; i <= k; i++) dp2[i] = dp[i - 1] + dp[i];
    for(int i = 1; i <= k; i++) dp2[i] *= i;
    dp = move(dp2);
    mint ans = 0;
    for(int i = 1; i <= k; i++) ans += dp1[i] * dp[i];
    ans *= all;
    cout << ans.val() << "\n";
  }
}