description: A subarray of array a from index l to the index r is the array [a_l, a_{l+1}, ..., a_{r}]. The number of occurrences of the array b in the array a is the number of subarrays of a such that they are equal to b.
  
  You are given n arrays A_1, A_2, ..., A_n; the elements of these arrays are integers from 1 to k. You have to build an array a consisting of m integers from 1 to k in such a way that, for every given subarray A_i, the number of occurrences of A_i in the array a is not less than the number of occurrences of each non-empty subarray of A_i in a. Note that if A_i doesn't occur in a, and no subarray of A_i occurs in a, this condition is still met for A_i.
  
  Your task is to calculate the number of different arrays a you can build, and print it modulo 998244353.
  
  Input
  
  The first line contains three integers n, m and k (1 ≤ n, m, k ≤ 3 ⋅ 10^5) — the number of the given arrays, the desired length of the array a, and the upper bound on the values in the arrays.
  
  Then n lines follow. The i-th line represents the array A_i. The first integer in the i-th line is c_i (1 ≤ c_i ≤ m) — the number of elements in A_i; then, c_i integers from 1 to k follow — the elements of the array A_i.
  
  Additional constraint on the input: ∑_{i=1}^n c_i ≤ 3 ⋅ 10^5; i. e., the number of elements in the given arrays in total does not exceed 3 ⋅ 10^5.
  
  Output
  
  Print one integer — the number of different arrays a you can build, taken modulo 998244353.
  
  Examples
  
  Input
  
  
  2 4 3
  2 1 2
  1 3
  
  
  Output
  
  
  5
  
  
  Input
  
  
  2 4 3
  2 1 2
  3 3 2 1
  
  
  Output
  
  
  0
  
  
  Input
  
  
  1 42 1337
  2 13 31
  
  
  Output
  
  
  721234447
solution: #include <bits/stdc++.h>
  using namespace std;
  template <typename T>
  T inverse(T a, T m) {
    T u = 0, v = 1;
    while (a != 0) {
      T t = m / a;
      m -= t * a;
      swap(a, m);
      u -= t * v;
      swap(u, v);
    }
    assert(m == 1);
    return u;
  }
  template <typename T>
  class Modular {
   public:
    using Type = typename decay<decltype(T::value)>::type;
    constexpr Modular() : value() {}
    template <typename U>
    Modular(const U &x) {
      value = normalize(x);
    }
    template <typename U>
    static Type normalize(const U &x) {
      Type v;
      if (-mod() <= x && x < mod())
        v = static_cast<Type>(x);
      else
        v = static_cast<Type>(x % mod());
      if (v < 0) v += mod();
      return v;
    }
    const Type &operator()() const { return value; }
    template <typename U>
    explicit operator U() const {
      return static_cast<U>(value);
    }
    constexpr static Type mod() { return T::value; }
    Modular &operator+=(const Modular &other) {
      if ((value += other.value) >= mod()) value -= mod();
      return *this;
    }
    Modular &operator-=(const Modular &other) {
      if ((value -= other.value) < 0) value += mod();
      return *this;
    }
    template <typename U>
    Modular &operator+=(const U &other) {
      return *this += Modular(other);
    }
    template <typename U>
    Modular &operator-=(const U &other) {
      return *this -= Modular(other);
    }
    Modular &operator++() { return *this += 1; }
    Modular &operator--() { return *this -= 1; }
    Modular operator++(int) {
      Modular result(*this);
      *this += 1;
      return result;
    }
    Modular operator--(int) {
      Modular result(*this);
      *this -= 1;
      return result;
    }
    Modular operator-() const { return Modular(-value); }
    template <typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                       Modular>::type &
    operator*=(const Modular &rhs) {
      value = normalize(static_cast<int64_t>(value) *
                        static_cast<int64_t>(rhs.value));
      return *this;
    }
    template <typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, long long>::value,
                       Modular>::type &
    operator*=(const Modular &rhs) {
      long long q = static_cast<long long>(static_cast<long double>(value) *
                                           rhs.value / mod());
      value = normalize(value * rhs.value - q * mod());
      return *this;
    }
    template <typename U = T>
    typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                       Modular>::type &
    operator*=(const Modular &rhs) {
      value = normalize(value * rhs.value);
      return *this;
    }
    Modular &operator/=(const Modular &other) {
      return *this *= Modular(inverse(other.value, mod()));
    }
    friend const Type &abs(const Modular &x) { return x.value; }
    template <typename U>
    friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);
    template <typename U>
    friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);
    template <typename V, typename U>
    friend V &operator>>(V &stream, Modular<U> &number);
  
   private:
    Type value;
  };
  template <typename T>
  bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) {
    return lhs.value == rhs.value;
  }
  template <typename T, typename U>
  bool operator==(const Modular<T> &lhs, U rhs) {
    return lhs == Modular<T>(rhs);
  }
  template <typename T, typename U>
  bool operator==(U lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) == rhs;
  }
  template <typename T>
  bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) {
    return !(lhs == rhs);
  }
  template <typename T, typename U>
  bool operator!=(const Modular<T> &lhs, U rhs) {
    return !(lhs == rhs);
  }
  template <typename T, typename U>
  bool operator!=(U lhs, const Modular<T> &rhs) {
    return !(lhs == rhs);
  }
  template <typename T>
  bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) {
    return lhs.value < rhs.value;
  }
  template <typename T>
  Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) += rhs;
  }
  template <typename T, typename U>
  Modular<T> operator+(const Modular<T> &lhs, U rhs) {
    return Modular<T>(lhs) += rhs;
  }
  template <typename T, typename U>
  Modular<T> operator+(U lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) += rhs;
  }
  template <typename T>
  Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) -= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator-(const Modular<T> &lhs, U rhs) {
    return Modular<T>(lhs) -= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator-(U lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) -= rhs;
  }
  template <typename T>
  Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) *= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator*(const Modular<T> &lhs, U rhs) {
    return Modular<T>(lhs) *= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator*(U lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) *= rhs;
  }
  template <typename T>
  Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) /= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator/(const Modular<T> &lhs, U rhs) {
    return Modular<T>(lhs) /= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator/(U lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) /= rhs;
  }
  template <typename T, typename U>
  Modular<T> power(const Modular<T> &a, const U &b) {
    assert(b >= 0);
    Modular<T> x = a, res = 1;
    U p = b;
    while (p > 0) {
      if (p & 1) res *= x;
      x *= x;
      p >>= 1;
    }
    return res;
  }
  template <typename T>
  bool IsZero(const Modular<T> &number) {
    return number() == 0;
  }
  template <typename T>
  string to_string(const Modular<T> &number) {
    return to_string(number());
  }
  template <typename U, typename T>
  U &operator<<(U &stream, const Modular<T> &number) {
    return stream << number();
  }
  template <typename U, typename T>
  U &operator>>(U &stream, Modular<T> &number) {
    typename common_type<typename Modular<T>::Type, long long>::type x;
    stream >> x;
    number.value = Modular<T>::normalize(x);
    return stream;
  }
  constexpr int md = (int)998244353;
  using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
  const int N = 3e5 + 5;
  int An, L, alpha;
  set<int> e[N];
  int indegree[N];
  bool vis[N];
  bool flag;
  int visited;
  void dfs(int at) {
    vis[at] = true;
    visited++;
    if (e[at].size() > 1) flag = false;
    for (int to : e[at]) {
      if (vis[to]) {
        flag = false;
        continue;
      }
      if (indegree[to] != 1) {
        flag = false;
      }
      dfs(to);
    }
  }
  int lengths[N];
  vector<pair<int, int>> recs;
  Mint dp[N];
  int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> An >> L >> alpha;
    for (int i = 1; i <= An; i++) {
      int c;
      cin >> c;
      vector<int> A(c);
      for (int &a : A) cin >> a;
      for (int j = 0; j < c - 1; j++) {
        int from = A[j];
        int to = A[j + 1];
        if (e[from].find(to) == e[from].end()) {
          e[from].insert(to);
          indegree[to]++;
        }
      }
    }
    for (int i = 1; i <= alpha; i++) {
      if (indegree[i] == 0) {
        assert(vis[i] == false);
        flag = true;
        visited = 0;
        dfs(i);
        if (flag) {
          lengths[visited]++;
        }
      }
    }
    for (int len = 1; len <= alpha; len++) {
      if (lengths[len]) {
        recs.push_back({len, lengths[len]});
      }
    }
    dp[0] = 1;
    for (int i = 1; i <= L; i++) {
      dp[i] = 0;
      for (auto [back, times] : recs) {
        if (i - back >= 0) {
          dp[i] += dp[i - back] * times;
        }
      }
    }
    cout << dp[L] << "\n";
    return 0;
  }
  