Problem p02960 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>

#ifdef _DEBUG
#define debug(x)                                                               \
  cerr << "line: " << __LINE__ << ", func: " << __func__ << " ->  " << #x      \
       << " = " << x << endl
#else
#define debug(x)
#endif

#define all(s) begin(s), end(s)
#define rall(s) rbegin(s), rend(s)
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define rrep(i, a, b) for (int i = ((a)-1); i >= (b); i--)
#define pb push_back
#define sz(a) int((a).size())

using namespace std;

using ll = long long;
using ull = unsigned long long;
using i_i = pair<int, int>;
using ll_ll = pair<ll, ll>;
using d_ll = pair<double, ll>;
using ll_d = pair<ll, double>;
using d_d = pair<double, double>;

static constexpr ll LL_INF = 1LL << 60;
static constexpr int I_INF = 1 << 28;
static constexpr double PI =
    static_cast<double>(3.14159265358979323846264338327950288);
static constexpr double EPS = numeric_limits<double>::epsilon();
static constexpr ll MOD = 1000000007;

static map<type_index, const char *const> scanType = {{typeid(int), "%d"},
                                                      {typeid(ll), "%lld"},
                                                      {typeid(double), "%lf"},
                                                      {typeid(char), "%c"}};

template <class T> static void scan(vector<T> &v);
[[maybe_unused]] static void scan(vector<string> &v, bool isWord = true);
template <class T> static inline bool chmax(T &a, T b);
template <class T> static inline bool chmin(T &a, T b);
template <class A, size_t N, class T>
static void Fill(A (&arr)[N], const T &val);

ll dp[100010][13];

int main(int argc, char *argv[]) {
  std::string s;
  std::cin >> s;
  dp[0][0] = 1;

  rep(i, 0, sz(s)) rep(m, 0, 13) {
    int first = (s[i] == '?' ? 0 : s[i] - '0');
    int last = (s[i] == '?' ? 10 : first + 1);
    rep(j, first, last) {
      int next_m = stoll(to_string(m) + char('0' + j)) % 13;
      dp[i + 1][next_m] += dp[i][m];
      dp[i + 1][next_m] %= MOD;
    }
  }

  cout << dp[sz(s)][5] << endl;
  return 0;
}

template <class T> static void scan(vector<T> &v) {
  auto tFormat = scanType[typeid(T)];
  for (T &n : v) {
    scanf(tFormat, &n);
  }
}

static void scan(vector<string> &v, bool isWord) {
  if (isWord) {
    for (auto &n : v) {
      cin >> n;
    }
    return;
  }

  int i = 0, size = v.size();
  string s;
  getline(cin, s);

  if (s.size() != 0) {
    i++;
    v[0] = s;
  }

  for (; i < size; ++i) {
    getline(cin, v[i]);
  }
}

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

template <class A, size_t N, class T> void Fill(A (&arr)[N], const T &val) {
  std::fill((T *)arr, (T *)(arr + N), val);
}


Fixed submission:
#include <bits/stdc++.h>

#ifdef _DEBUG
#define debug(x)                                                               \
  cerr << "line: " << __LINE__ << ", func: " << __func__ << " ->  " << #x      \
       << " = " << x << endl
#else
#define debug(x)
#endif

#define all(s) begin(s), end(s)
#define rall(s) rbegin(s), rend(s)
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define rrep(i, a, b) for (int i = ((a)-1); i >= (b); i--)
#define pb push_back
#define sz(a) int((a).size())

using namespace std;

using ll = long long;
using ull = unsigned long long;
using i_i = pair<int, int>;
using ll_ll = pair<ll, ll>;
using d_ll = pair<double, ll>;
using ll_d = pair<ll, double>;
using d_d = pair<double, double>;

static constexpr ll LL_INF = 1LL << 60;
static constexpr int I_INF = 1 << 28;
static constexpr double PI =
    static_cast<double>(3.14159265358979323846264338327950288);
static constexpr double EPS = numeric_limits<double>::epsilon();
static constexpr ll MOD = 1000000007;

static map<type_index, const char *const> scanType = {{typeid(int), "%d"},
                                                      {typeid(ll), "%lld"},
                                                      {typeid(double), "%lf"},
                                                      {typeid(char), "%c"}};

template <class T> static void scan(vector<T> &v);
[[maybe_unused]] static void scan(vector<string> &v, bool isWord = true);
template <class T> static inline bool chmax(T &a, T b);
template <class T> static inline bool chmin(T &a, T b);
template <class A, size_t N, class T>
static void Fill(A (&arr)[N], const T &val);

ll dp[100010][13];

int main(int argc, char *argv[]) {
  std::string s;
  std::cin >> s;
  dp[0][0] = 1;

  rep(i, 0, sz(s)) rep(m, 0, 13) {
    int first = (s[i] == '?' ? 0 : s[i] - '0');
    int last = (s[i] == '?' ? 10 : first + 1);
    rep(j, first, last) {
      int next_m = ((m * 10) + j) % 13;
      dp[i + 1][next_m] = (dp[i + 1][next_m] + dp[i][m]) % MOD;
    }
  }

  cout << dp[sz(s)][5] << endl;
  return 0;
}

template <class T> static void scan(vector<T> &v) {
  auto tFormat = scanType[typeid(T)];
  for (T &n : v) {
    scanf(tFormat, &n);
  }
}

static void scan(vector<string> &v, bool isWord) {
  if (isWord) {
    for (auto &n : v) {
      cin >> n;
    }
    return;
  }

  int i = 0, size = v.size();
  string s;
  getline(cin, s);

  if (s.size() != 0) {
    i++;
    v[0] = s;
  }

  for (; i < size; ++i) {
    getline(cin, v[i]);
  }
}

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

template <class A, size_t N, class T> void Fill(A (&arr)[N], const T &val) {
  std::fill((T *)arr, (T *)(arr + N), val);
}