Problem p01944 (C++) — buggy submission, verdict: Time Limit Exceeded

// need
#include <algorithm>
#include <iostream>

// data structure
#include <bitset>
// #include <list>
#include <array>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <tuple>
// #include <unordered_map>
#include <complex>
#include <unordered_set>
// #include <deque>
#include <valarray>

// stream
// #include <istream>
// #include <sstream>
// #include <ostream>
// #include <fstream>

// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
// #include <typeinfo>
#include <chrono>
#include <numeric>
#include <random>

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { std::cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int i = 0; i < n; ++i) {                                                \\
    MACRO_VEC_ROW_Scan(i, __VA_ARGS__);                                        \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { std::cin >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    std::cin >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &r : c)                                                            \\
    for (auto &i : r)                                                          \\
      std::cin >> i;

// output
#define OUT(d) std::cout << d;
#define FOUT(n, d) std::cout << std::fixed << std::setprecision(n) << d;
#define SOUT(n, c, d) std::cout << std::setw(n) << std::setfill(c) << d;
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define SPBR(i, n) std::cout << (i + 1 == n ? '\\n' : ' ');
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define SHOW(d)                                                                \\
  { std::cerr << #d << "\\t:" << d << "\\n"; }
#define SHOWVECTOR(v)                                                          \\
  {                                                                            \\
    std::cerr << #v << "\\t:";                                                  \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx << " ";                                                 \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOWVECTOR2(v)                                                         \\
  {                                                                            \\
    std::cerr << #v << "\\t:\\n";                                                \\
    for (const auto &xxx : v) {                                                \\
      for (const auto &yyy : xxx) {                                            \\
        std::cerr << yyy << " ";                                               \\
      }                                                                        \\
      std::cerr << "\\n";                                                       \\
    }                                                                          \\
  }
#define SHOWQUEUE(a)                                                           \\
  {                                                                            \\
    auto tmp(a);                                                               \\
    std::cerr << #a << "\\t:";                                                  \\
    while (!tmp.empty()) {                                                     \\
      std::cerr << tmp.front() << " ";                                         \\
      tmp.pop();                                                               \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }

// utility
#define ALL(a) (a).begin(), (a).end()
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define RREP(i, n) for (int i = int(n) - 1; i >= 0; --i)
#define FORLL(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define RFORLL(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define REPLL(i, n) for (ll i = 0; i < ll(n); ++i)
#define RREPLL(i, n) for (ll i = ll(n) - 1; i >= 0; --i)
#define IN(a, x, b) (a <= x && x < b)
template <typename T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
#define EXCEPTION(msg)                                                         \\
  throw std::string("Exception : " msg " [ in ") + __func__ + " : " +          \\
      std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg)                                                         \\
  try {                                                                        \\
    if (cond)                                                                  \\
      EXCEPTION(msg);                                                          \\
  } catch (std::string s) {                                                    \\
    std::cerr << s << std::endl;                                               \\
  }
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\\n";
}

// test
template <class T> std::vector<std::vector<T>> VV(int n) {
  return std::vector<std::vector<T>>(n);
}
template <class T> std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
  return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}

// type/const

#define int ll
using ll = long long;
using ull = unsigned long long;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                         // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

ll powMod(ll n, ll p, ll mod) {
  ll res = 1;
  while (p) {
    if (p & 1)
      res *= n;
    res %= mod;
    n *= n;
    n %= mod;
    p >>= 1;
  }
  return res;
}

std::vector<int> mul(const std::vector<int> &l, const std::vector<int> &r) {
  int n = l.size();
  std::vector<int> res(n, 0);
  REP(i, n) {
    REP(j, n) { (res[i] += l[j] * r[(i - j + n) % n]) %= MOD; }
  }
  return res;
}

signed main() {
  INIT;
  VAR(int, n, m, k);
  VEC(int, p, m);
  p.emplace_back(0);
  REP(i, m) p[i] %= n;
  std::vector<int> C(n, 0);
  REP(i, m + 1)++ C[p[i]];
  std::vector<int> B(n, 0);
  B[0] = 1;

  while (k) {
    if (k & 1)
      B = mul(B, C);
    C = mul(C, C);
    k >>= 1;
  }
  REP(i, n) { OUT(B[i]) BR; }
  return 0;
}

Error: TLE

Fixed submission:

// need
#include <algorithm>
#include <iostream>

// data structure
#include <bitset>
// #include <list>
#include <array>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <tuple>
// #include <unordered_map>
#include <complex>
#include <unordered_set>
// #include <deque>
#include <valarray>

// stream
// #include <istream>
// #include <sstream>
// #include <ostream>
// #include <fstream>

// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
// #include <typeinfo>
#include <chrono>
#include <numeric>
#include <random>

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { std::cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int i = 0; i < n; ++i) {                                                \\
    MACRO_VEC_ROW_Scan(i, __VA_ARGS__);                                        \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { std::cin >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    std::cin >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &r : c)                                                            \\
    for (auto &i : r)                                                          \\
      std::cin >> i;

// output
#define OUT(d) std::cout << d;
#define FOUT(n, d) std::cout << std::fixed << std::setprecision(n) << d;
#define SOUT(n, c, d) std::cout << std::setw(n) << std::setfill(c) << d;
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define SPBR(i, n) std::cout << (i + 1 == n ? '\\n' : ' ');
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define SHOW(d)                                                                \\
  { std::cerr << #d << "\\t:" << d << "\\n"; }
#define SHOWVECTOR(v)                                                          \\
  {                                                                            \\
    std::cerr << #v << "\\t:";                                                  \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx << " ";                                                 \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOWVECTOR2(v)                                                         \\
  {                                                                            \\
    std::cerr << #v << "\\t:\\n";                                                \\
    for (const auto &xxx : v) {                                                \\
      for (const auto &yyy : xxx) {                                            \\
        std::cerr << yyy << " ";                                               \\
      }                                                                        \\
      std::cerr << "\\n";                                                       \\
    }                                                                          \\
  }
#define SHOWQUEUE(a)                                                           \\
  {                                                                            \\
    auto tmp(a);                                                               \\
    std::cerr << #a << "\\t:";                                                  \\
    while (!tmp.empty()) {                                                     \\
      std::cerr << tmp.front() << " ";                                         \\
      tmp.pop();                                                               \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }

// utility
#define ALL(a) (a).begin(), (a).end()
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define RREP(i, n) for (int i = int(n) - 1; i >= 0; --i)
#define FORLL(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define RFORLL(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define REPLL(i, n) for (ll i = 0; i < ll(n); ++i)
#define RREPLL(i, n) for (ll i = ll(n) - 1; i >= 0; --i)
#define IN(a, x, b) (a <= x && x < b)
template <typename T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
#define EXCEPTION(msg)                                                         \\
  throw std::string("Exception : " msg " [ in ") + __func__ + " : " +          \\
      std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg)                                                         \\
  try {                                                                        \\
    if (cond)                                                                  \\
      EXCEPTION(msg);                                                          \\
  } catch (std::string s) {                                                    \\
    std::cerr << s << std::endl;                                               \\
  }
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\\n";
}

// test
template <class T> std::vector<std::vector<T>> VV(int n) {
  return std::vector<std::vector<T>>(n);
}
template <class T> std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
  return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}

// type/const

#define int ll
using ll = long long;
using ull = unsigned long long;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                         // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

template <class T> class Matrix_MOD {
private:
  std::valarray<std::valarray<T>> mat;

public:
  Matrix_MOD(size_t m = 0, size_t n = 0, T init = 0) {
    if (n == 0)
      n = m;
    mat.resize(m);
    for (size_t i = 0; i < m; ++i)
      mat[i].resize(n, init);
  }
  Matrix_MOD(std::valarray<std::valarray<T>> a) { mat = a; }
  Matrix_MOD<T> init(size_t m = 0, size_t n = 0, T init = 0) {
    if (n == 0)
      n = m;
    mat.resize(m);
    for (size_t i = 0; i < m; ++i)
      mat[i].resize(n, init);
    return *this;
  }
  std::valarray<T> &operator[](size_t i) { return mat[i]; }
  const std::valarray<T> &operator[](size_t i) const { return mat[i]; }
  Matrix_MOD<T> &operator=(const Matrix_MOD<T> &r) {
    for (size_t i = 0; i < mat.size(); ++i)
      mat[i] = r[i];
    return *this;
  }
  Matrix_MOD<T> operator+() const { return mat; }
  Matrix_MOD<T> operator-() const {
    Matrix_MOD<T> res(mat.size());
    for (size_t i = 0; i < mat.size(); ++i)
      res[i] = (MOD - mat[i]) %= MOD;
    return res;
  }
  Matrix_MOD<T> &operator+=(const Matrix_MOD<T> &r) {
    for (size_t i = 0; i < mat.size(); ++i)
      (mat[i] += r[i]) %= MOD;
    return *this;
  }
  Matrix_MOD<T> &operator+=(const T &x) {
    for (size_t i = 0; i < mat.size(); ++i)
      (mat[i] += x) %= MOD;
    return *this;
  }
  Matrix_MOD<T> &operator-=(const Matrix_MOD<T> &r) { return *this += MOD - r; }
  Matrix_MOD<T> &operator-=(const T &x) { return *this += MOD - x; }
  Matrix_MOD<T> &operator*=(const Matrix_MOD<T> &r) { // O(N^3)
    Matrix_MOD<T> res(*this);
    for (size_t i = 0; i < mat.size(); ++i) {
      for (size_t j = 0; j < r[0].size(); ++j) {
        res[i][j] = 0;
        for (size_t k = 0; k < mat[0].size(); ++k) {
          (res[i][j] += mat[i][k] * r[k][j] % MOD) %= MOD;
        }
      }
    }
    return *this = res;
  }
  Matrix_MOD<T> &operator*=(const T &x) {
    for (size_t i = 0; i < mat.size(); ++i)
      (mat[i] *= x) %= MOD;
    return *this;
  }
  Matrix_MOD<T> &operator%=(const T &mod) {
    for (size_t i = 0; i < mat.size(); ++i)
      mat[i] %= MOD;
    return *this;
  }
  Matrix_MOD<T> &operator^=(ll p) { // O(N^3 logP)
    Matrix_MOD<T> res(*this);

    for (size_t i = 0; i < mat.size(); ++i) {
      for (size_t j = 0; j < mat[0].size(); ++j) {
        res[i][j] = i == j;
      }
    }
    while (p) {
      if (p & 1)
        (res *= (*this)) %= MOD;
      ((*this) *= (*this)) %= MOD;
      p >>= 1;
    }
    for (size_t i = 0; i < mat.size(); ++i)
      mat[i] = res[i];
    return *this;
  }
  Matrix_MOD<T> operator+(const Matrix_MOD &r) const {
    Matrix_MOD<T> res(mat);
    return res += r;
  }
  Matrix_MOD<T> operator-(const Matrix_MOD &r) const {
    Matrix_MOD<T> res(mat);
    return res -= r;
  }
  Matrix_MOD<T> operator*(const Matrix_MOD &r) const {
    Matrix_MOD<T> res(mat);
    return res *= r;
  }
  Matrix_MOD<T> operator*(const T &r) const {
    Matrix_MOD<T> res(mat);
    return res *= r;
  }
  Matrix_MOD<T> operator^(const int &p) const {
    Matrix_MOD<T> res(mat);
    return res ^= p;
  }
  Matrix_MOD<T> t() const {
    Matrix_MOD<T> res(mat[0].size(), mat.size(), 0);
    for (size_t i = 0; i < mat[0].size(); ++i) {
      for (size_t j = 0; j < mat.size(); ++j) {
        res[i][j] = mat[j][i];
      }
    }
    return res;
  }
  static Matrix_MOD<T> getUnit(size_t n) {
    Matrix_MOD<T> res(n, n, 0);
    for (size_t i = 0; i < n; ++i)
      res[i][i] = 1;
    return res;
  }
  void show() const {
    for (const auto &r : mat) {
      for (const auto &x : r) {
        std::cerr << x << "\\t";
      }
      std::cerr << std::endl;
    }
  }
};

signed main() {
  INIT;
  VAR(int, n, m, k);
  VEC(int, p, m);
  p.emplace_back(0);
  REP(i, m) p[i] %= n;
  std::vector<int> C(n, 0);
  REP(i, m + 1)++ C[p[i]];
  Matrix_MOD<int> A(n, n, 0);
  REP(i, n) REP(j, n) { A[i][(i + j) % n] = C[j]; }
  A ^= k;
  REP(i, n) { OUT(A[0][i]) BR; }
  return 0;
}