Problem p02539 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
const int MOD = 998244353;

int sum(int a, int b) { return a + b >= MOD ? a + b - MOD : a + b; }
int sub(int a, int b) { return a - b < 0 ? a - b + MOD : a - b; }
int mul(int a, int b) { return (1LL * a * b) % MOD; }
int pwr(int a, int b) {
  if (!b)
    return 1;
  int r = pwr(a, b / 2);
  r = mul(r, r);
  if (b % 2)
    r = mul(r, a);
  return r;
}

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
  x %= m;
  if (x < 0)
    x += m;
  return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
  unsigned int _m;
  unsigned long long im;

  // @param m `1 <= m < 2^31`
  barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

  // @return m
  unsigned int umod() const { return _m; }

  // @param a `0 <= a < m`
  // @param b `0 <= b < m`
  // @return `a * b % m`
  unsigned int mul(unsigned int a, unsigned int b) const {
    // [1] m = 1
    // a = b = im = 0, so okay

    // [2] m >= 2
    // im = ceil(2^64 / m)
    // -> im * m = 2^64 + r (0 <= r < m)
    // let z = a*b = c*m + d (0 <= c, d < m)
    // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
    // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) <
    // 2^64 * 2
    // ((ab * im) >> 64) == c or c + 1
    unsigned long long z = a;
    z *= b;
#ifdef _MSC_VER
    unsigned long long x;
    _umul128(z, im, &x);
#else
    unsigned long long x =
        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
    unsigned int v = (unsigned int)(z - x * _m);
    if (_m <= v)
      v += _m;
    return v;
  }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
  if (m == 1)
    return 0;
  unsigned int _m = (unsigned int)(m);
  unsigned long long r = 1;
  unsigned long long y = safe_mod(x, m);
  while (n) {
    if (n & 1)
      r = (r * y) % _m;
    y = (y * y) % _m;
    n >>= 1;
  }
  return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
  if (n <= 1)
    return false;
  if (n == 2 || n == 7 || n == 61)
    return true;
  if (n % 2 == 0)
    return false;
  long long d = n - 1;
  while (d % 2 == 0)
    d /= 2;
  constexpr long long bases[3] = {2, 7, 61};
  for (long long a : bases) {
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
  a = safe_mod(a, b);
  if (a == 0)
    return {b, 0};

  // Contracts:
  // [1] s - m0 * a = 0 (mod b)
  // [2] t - m1 * a = 0 (mod b)
  // [3] s * |m1| + t * |m0| <= b
  long long s = b, t = a;
  long long m0 = 0, m1 = 1;

  while (t) {
    long long u = s / t;
    s -= t * u;
    m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b

    // [3]:
    // (s - t * u) * |m1| + t * |m0 - m1 * u|
    // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
    // = s * |m1| + t * |m0| <= b

    auto tmp = s;
    s = t;
    t = tmp;
    tmp = m0;
    m0 = m1;
    m1 = tmp;
  }
  // by [3]: |m0| <= b/g
  // by g != b: |m0| < b/g
  if (m0 < 0)
    m0 += b / s;
  return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
  if (m == 2)
    return 1;
  if (m == 167772161)
    return 3;
  if (m == 469762049)
    return 3;
  if (m == 754974721)
    return 11;
  if (m == 998244353)
    return 3;
  int divs[20] = {};
  divs[0] = 2;
  int cnt = 1;
  int x = (m - 1) / 2;
  while (x % 2 == 0)
    x /= 2;
  for (int i = 3; (long long)(i)*i <= x; i += 2) {
    if (x % i == 0) {
      divs[cnt++] = i;
      while (x % i == 0) {
        x /= i;
      }
    }
  }
  if (x > 1) {
    divs[cnt++] = x;
  }
  for (int g = 2;; g++) {
    bool ok = true;
    for (int i = 0; i < cnt; i++) {
      if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
        ok = false;
        break;
      }
    }
    if (ok)
      return g;
  }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

} // namespace internal

} // namespace atcoder

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value ||
                                  is_signed_int128<T>::value ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_signed_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_signed<T>::value) ||
                                  is_signed_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value, make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using to_unsigned =
    typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

} // namespace internal

} // namespace atcoder

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

} // namespace internal

template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
  using mint = static_modint;

public:
  static constexpr int mod() { return m; }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }

  static_modint() : _v(0) {}
  template <class T, internal::is_signed_int_t<T> * = nullptr>
  static_modint(T v) {
    long long x = (long long)(v % (long long)(umod()));
    if (x < 0)
      x += umod();
    _v = (unsigned int)(x);
  }
  template <class T, internal::is_unsigned_int_t<T> * = nullptr>
  static_modint(T v) {
    _v = (unsigned int)(v % umod());
  }
  static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }

  unsigned int val() const { return _v; }

  mint &operator++() {
    _v++;
    if (_v == umod())
      _v = 0;
    return *this;
  }
  mint &operator--() {
    if (_v == 0)
      _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }

  mint &operator+=(const mint &rhs) {
    _v += rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint &operator-=(const mint &rhs) {
    _v -= rhs._v;
    if (_v >= umod())
      _v += umod();
    return *this;
  }
  mint &operator*=(const mint &rhs) {
    unsigned long long z = _v;
    z *= rhs._v;
    _v = (unsigned int)(z % umod());
    return *this;
  }
  mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }

  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1)
        r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    if (prime) {
      assert(_v);
      return pow(umod() - 2);
    } else {
      auto eg = internal::inv_gcd(_v, m);
      assert(eg.first == 1);
      return eg.second;
    }
  }

  friend mint operator+(const mint &lhs, const mint &rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint &lhs, const mint &rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint &lhs, const mint &rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint &lhs, const mint &rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint &lhs, const mint &rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint &lhs, const mint &rhs) {
    return lhs._v != rhs._v;
  }

private:
  unsigned int _v;
  static constexpr unsigned int umod() { return m; }
  static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
  using mint = dynamic_modint;

public:
  static int mod() { return (int)(bt.umod()); }
  static void set_mod(int m) {
    assert(1 <= m);
    bt = internal::barrett(m);
  }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }

  dynamic_modint() : _v(0) {}
  template <class T, internal::is_signed_int_t<T> * = nullptr>
  dynamic_modint(T v) {
    long long x = (long long)(v % (long long)(mod()));
    if (x < 0)
      x += mod();
    _v = (unsigned int)(x);
  }
  template <class T, internal::is_unsigned_int_t<T> * = nullptr>
  dynamic_modint(T v) {
    _v = (unsigned int)(v % mod());
  }
  dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }

  unsigned int val() const { return _v; }

  mint &operator++() {
    _v++;
    if (_v == umod())
      _v = 0;
    return *this;
  }
  mint &operator--() {
    if (_v == 0)
      _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }

  mint &operator+=(const mint &rhs) {
    _v += rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint &operator-=(const mint &rhs) {
    _v += mod() - rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint &operator*=(const mint &rhs) {
    _v = bt.mul(_v, rhs._v);
    return *this;
  }
  mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }

  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1)
        r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    auto eg = internal::inv_gcd(_v, mod());
    assert(eg.first == 1);
    return eg.second;
  }

  friend mint operator+(const mint &lhs, const mint &rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint &lhs, const mint &rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint &lhs, const mint &rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint &lhs, const mint &rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint &lhs, const mint &rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint &lhs, const mint &rhs) {
    return lhs._v != rhs._v;
  }

private:
  unsigned int _v;
  static internal::barrett bt;
  static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

} // namespace internal

} // namespace atcoder

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
  int x = 0;
  while ((1U << x) < (unsigned int)(n))
    x++;
  return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
  unsigned long index;
  _BitScanForward(&index, n);
  return index;
#else
  return __builtin_ctz(n);
#endif
}

} // namespace internal

} // namespace atcoder

namespace atcoder {

namespace internal {

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly(std::vector<mint> &a) {
  static constexpr int g = internal::primitive_root<mint::mod()>;
  int n = int(a.size());
  int h = internal::ceil_pow2(n);

  static bool first = true;
  static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
  if (first) {
    first = false;
    mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
    int cnt2 = bsf(mint::mod() - 1);
    mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
    for (int i = cnt2; i >= 2; i--) {
      // e^(2^i) == 1
      es[i - 2] = e;
      ies[i - 2] = ie;
      e *= e;
      ie *= ie;
    }
    mint now = 1;
    for (int i = 0; i <= cnt2 - 2; i++) {
      sum_e[i] = es[i] * now;
      now *= ies[i];
    }
  }
  for (int ph = 1; ph <= h; ph++) {
    int w = 1 << (ph - 1), p = 1 << (h - ph);
    mint now = 1;
    for (int s = 0; s < w; s++) {
      int offset = s << (h - ph + 1);
      for (int i = 0; i < p; i++) {
        auto l = a[i + offset];
        auto r = a[i + offset + p] * now;
        a[i + offset] = l + r;
        a[i + offset + p] = l - r;
      }
      now *= sum_e[bsf(~(unsigned int)(s))];
    }
  }
}

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly_inv(std::vector<mint> &a) {
  static constexpr int g = internal::primitive_root<mint::mod()>;
  int n = int(a.size());
  int h = internal::ceil_pow2(n);

  static bool first = true;
  static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
  if (first) {
    first = false;
    mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
    int cnt2 = bsf(mint::mod() - 1);
    mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
    for (int i = cnt2; i >= 2; i--) {
      // e^(2^i) == 1
      es[i - 2] = e;
      ies[i - 2] = ie;
      e *= e;
      ie *= ie;
    }
    mint now = 1;
    for (int i = 0; i <= cnt2 - 2; i++) {
      sum_ie[i] = ies[i] * now;
      now *= es[i];
    }
  }

  for (int ph = h; ph >= 1; ph--) {
    int w = 1 << (ph - 1), p = 1 << (h - ph);
    mint inow = 1;
    for (int s = 0; s < w; s++) {
      int offset = s << (h - ph + 1);
      for (int i = 0; i < p; i++) {
        auto l = a[i + offset];
        auto r = a[i + offset + p];
        a[i + offset] = l + r;
        a[i + offset + p] =
            (unsigned long long)(mint::mod() + l.val() - r.val()) * inow.val();
      }
      inow *= sum_ie[bsf(~(unsigned int)(s))];
    }
  }
}

} // namespace internal

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m)
    return {};
  if (std::min(n, m) <= 60) {
    if (n < m) {
      std::swap(n, m);
      std::swap(a, b);
    }
    std::vector<mint> ans(n + m - 1);
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        ans[i + j] += a[i] * b[j];
      }
    }
    return ans;
  }
  int z = 1 << internal::ceil_pow2(n + m - 1);
  a.resize(z);
  internal::butterfly(a);
  b.resize(z);
  internal::butterfly(b);
  for (int i = 0; i < z; i++) {
    a[i] *= b[i];
  }
  internal::butterfly_inv(a);
  a.resize(n + m - 1);
  mint iz = mint(z).inv();
  for (int i = 0; i < n + m - 1; i++)
    a[i] *= iz;
  return a;
}

template <unsigned int mod = 998244353, class T,
          std::enable_if_t<internal::is_integral<T>::value> * = nullptr>
std::vector<T> convolution(const std::vector<T> &a, const std::vector<T> &b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m)
    return {};

  using mint = static_modint<mod>;
  std::vector<mint> a2(n), b2(m);
  for (int i = 0; i < n; i++) {
    a2[i] = mint(a[i]);
  }
  for (int i = 0; i < m; i++) {
    b2[i] = mint(b[i]);
  }
  auto c2 = convolution(move(a2), move(b2));
  std::vector<T> c(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    c[i] = c2[i].val();
  }
  return c;
}

std::vector<long long> convolution_ll(const std::vector<long long> &a,
                                      const std::vector<long long> &b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m)
    return {};

  static constexpr unsigned long long MOD1 = 754974721; // 2^24
  static constexpr unsigned long long MOD2 = 167772161; // 2^25
  static constexpr unsigned long long MOD3 = 469762049; // 2^26
  static constexpr unsigned long long M2M3 = MOD2 * MOD3;
  static constexpr unsigned long long M1M3 = MOD1 * MOD3;
  static constexpr unsigned long long M1M2 = MOD1 * MOD2;
  static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

  static constexpr unsigned long long i1 =
      internal::inv_gcd(MOD2 * MOD3, MOD1).second;
  static constexpr unsigned long long i2 =
      internal::inv_gcd(MOD1 * MOD3, MOD2).second;
  static constexpr unsigned long long i3 =
      internal::inv_gcd(MOD1 * MOD2, MOD3).second;

  auto c1 = convolution<MOD1>(a, b);
  auto c2 = convolution<MOD2>(a, b);
  auto c3 = convolution<MOD3>(a, b);

  std::vector<long long> c(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    unsigned long long x = 0;
    x += (c1[i] * i1) % MOD1 * M2M3;
    x += (c2[i] * i2) % MOD2 * M1M3;
    x += (c3[i] * i3) % MOD3 * M1M2;
    // B = 2^63, -B <= x, r(real value) < B
    // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
    // r = c1[i] (mod MOD1)
    // focus on MOD1
    // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
    // r = x,
    //     x - M' + (0 or 2B),
    //     x - 2M' + (0, 2B or 4B),
    //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
    // (r - x) = 0, (0)
    //           - M' + (0 or 2B), (1)
    //           -2M' + (0 or 2B or 4B), (2)
    //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
    // we checked that
    //   ((1) mod MOD1) mod 5 = 2
    //   ((2) mod MOD1) mod 5 = 3
    //   ((3) mod MOD1) mod 5 = 4
    long long diff =
        c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
    if (diff < 0)
      diff += MOD1;
    static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3,
                                                     3 * M1M2M3};
    x -= offset[diff % 5];
    c[i] = x;
  }

  return c;
}

} // namespace atcoder

using namespace atcoder;
using mint = modint998244353;

const int MAXX = 1e5 + 7;
int fact[MAXX], ifact[MAXX];

int nCr(int n, int r) {
  if (r < 0 || n < r)
    return 0;
  return mul(fact[n], mul(ifact[r], ifact[n - r]));
}

int fr[MAXX];
int pinv[MAXX];
int dfact[MAXX];

vector<vector<mint>> w;
typedef pair<int, int> PII;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  fact[0] = 1;
  for (int i = 1; i < MAXX; i++)
    fact[i] = mul(i, fact[i - 1]);
  ifact[MAXX - 1] = pwr(fact[MAXX - 1], MOD - 2);
  for (int i = MAXX - 2; i >= 0; i--)
    ifact[i] = mul(i + 1, ifact[i + 1]);

  pinv[0] = 1;
  pinv[1] = pwr(2, MOD - 2);
  for (int i = 2; i < MAXX; i++)
    pinv[i] = mul(pinv[i - 1], pinv[1]);

  dfact[0] = 1;
  for (int i = 2; i < MAXX; i += 2)
    dfact[i] = mul(dfact[i - 2], i - 1);

  int n;
  cin >> n;

  for (int i = 0; i < n + n; i++) {
    int h;
    cin >> h;
    fr[h]++;
  }

  priority_queue<PII> pq;
  for (int i = 1; i < MAXX; i++) {
    if (fr[i] == 0)
      continue;
    w.emplace_back();
    for (int j = 0; j + j <= fr[i]; j++) {
      w.back().push_back(
          mul(fact[fr[i]], mul(ifact[j], mul(ifact[fr[i] - j - j], pinv[j]))));
    }
    if (w.size() > 1 && w.back().size() == 1) {
      w.pop_back();
    } else {
      pq.emplace(-w.size(), w.size() - 1);
    }
  }

  while (pq.size() > 1) {
    PII u = pq.top();
    pq.pop();
    PII v = pq.top();
    pq.pop();
    w[u.second] = convolution(w[u.second], w[v.second]);
    //        w[u.second] = ntt.multiply(w[u.second], w[v.second]);
    while (w[u.second].size() > 1 && w[u.second].back() == 0)
      w[u.second].pop_back();
    pq.emplace(-w[u.second].size(), u.second);
  }

  int z = pq.top().second;
  //    for (int i = 0; i < w[z].size(); i++) {
  //        cout << "ways[" << i << "] = " << w[z][i] << endl;
  //    }

  int ans = 0;
  for (int i = 0; i <= n && i < w[z].size(); i++) {
    int tmp = mul(w[z][i].val(), dfact[(n - i) * 2]);
    if (i & 1)
      ans = sub(ans, tmp);
    else
      ans = sum(ans, tmp);
  }

  cout << ans << "\\n";

  return 0;
}


Error: TLE

Fixed submission:

#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")

#include <bits/stdc++.h>
using namespace std;
const int MOD = 998244353;

int sum(int a, int b) { return a + b >= MOD ? a + b - MOD : a + b; }
int sub(int a, int b) { return a - b < 0 ? a - b + MOD : a - b; }
int mul(int a, int b) { return (1LL * a * b) % MOD; }
int pwr(int a, int b) {
  if (!b)
    return 1;
  int r = pwr(a, b / 2);
  r = mul(r, r);
  if (b % 2)
    r = mul(r, a);
  return r;
}

struct NTT {
  int N;
  vector<int> perm;
  int root, inv, pw;
  int invSz;
  NTT(int root, int inv, int pw) : root(root), inv(inv), pw(pw) {}
  void precalculate() {
    perm.resize(N);
    perm[0] = 0;
    for (int k = 1; k < N; k <<= 1) {
      for (int i = 0; i < k; i++) {
        perm[i] <<= 1;
        perm[i + k] = 1 + perm[i];
      }
    }
    invSz = pwr(N, MOD - 2);
  }
  void fft(vector<int> &v, bool invert = false) {
    if (v.size() != perm.size()) {
      N = v.size();
      assert(N && (N & (N - 1)) == 0);
      precalculate();
    }
    for (int i = 0; i < N; i++)
      if (i < perm[i])
        swap(v[i], v[perm[i]]);
    for (int len = 2; len <= N; len <<= 1) {
      int factor = invert ? inv : root;
      for (int i = len; i < pw; i <<= 1)
        factor = mul(factor, factor);
      for (int i = 0; i < N; i += len) {
        int w = 1;
        for (int j = 0; j < len / 2; j++) {
          int x = v[i + j], y = mul(w, v[i + j + len / 2]);
          v[i + j] = sum(x, y);
          v[i + j + len / 2] = sub(x, y);
          w = mul(w, factor);
        }
      }
    }
    if (invert) {
      for (int &x : v)
        x = mul(x, invSz);
    }
  }
  vector<int> multiply(vector<int> a, vector<int> b) {
    int n = 1;
    while (n < a.size() + b.size())
      n <<= 1;
    a.resize(n);
    b.resize(n);
    fft(a);
    fft(b);
    for (int i = 0; i < n; i++)
      a[i] = mul(a[i], b[i]);
    fft(a, true);
    return a;
  }
};

NTT ntt(15311432, 469870224, 1 << 23);

const int MAXX = 1e5 + 7;
int fact[MAXX], ifact[MAXX];

int nCr(int n, int r) {
  if (r < 0 || n < r)
    return 0;
  return mul(fact[n], mul(ifact[r], ifact[n - r]));
}

int fr[MAXX];
int pinv[MAXX];
int dfact[MAXX];

vector<vector<int>> w;
typedef pair<int, int> PII;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  fact[0] = 1;
  for (int i = 1; i < MAXX; i++)
    fact[i] = mul(i, fact[i - 1]);
  ifact[MAXX - 1] = pwr(fact[MAXX - 1], MOD - 2);
  for (int i = MAXX - 2; i >= 0; i--)
    ifact[i] = mul(i + 1, ifact[i + 1]);

  pinv[0] = 1;
  pinv[1] = pwr(2, MOD - 2);
  for (int i = 2; i < MAXX; i++)
    pinv[i] = mul(pinv[i - 1], pinv[1]);

  dfact[0] = 1;
  for (int i = 2; i < MAXX; i += 2)
    dfact[i] = mul(dfact[i - 2], i - 1);

  int n;
  cin >> n;

  for (int i = 0; i < n + n; i++) {
    int h;
    cin >> h;
    fr[h]++;
  }

  priority_queue<PII> pq;
  for (int i = 1; i < MAXX; i++) {
    if (fr[i] == 0)
      continue;
    w.emplace_back();
    for (int j = 0; j + j <= fr[i]; j++) {
      w.back().push_back(
          mul(fact[fr[i]], mul(ifact[j], mul(ifact[fr[i] - j - j], pinv[j]))));
    }
    if (w.size() > 1 && w.back().size() == 1) {
      w.pop_back();
    } else {
      pq.emplace(-w.size(), w.size() - 1);
    }
  }

  while (pq.size() > 1) {
    PII u = pq.top();
    pq.pop();
    PII v = pq.top();
    pq.pop();
    w[u.second] = ntt.multiply(w[u.second], w[v.second]);
    while (w[u.second].size() > 1 && w[u.second].back() == 0)
      w[u.second].pop_back();
    pq.emplace(-w[u.second].size(), u.second);
  }

  int z = pq.top().second;
  //    for (int i = 0; i < w[z].size(); i++) {
  //        cout << "ways[" << i << "] = " << w[z][i] << endl;
  //    }

  int ans = 0;
  for (int i = 0; i <= n && i < w[z].size(); i++) {
    int tmp = mul(w[z][i], dfact[(n - i) * 2]);
    if (i & 1)
      ans = sub(ans, tmp);
    else
      ans = sum(ans, tmp);
  }

  cout << ans << "\\n";

  return 0;
}