Problem p02960 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#include <numeric>
#include <vector>
#define PI 3.14159265358979323846
#define MAXINF (1e18L)
#define INF (1e9L)
#define EPS (1e-9)
#define MOD ((ll)(1e9 + 7))
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define Rep(i, sta, n) for (int i = sta; i < n; i++)
#define RREP(i, n) for (int i = int(n) - 1; i >= 0; --i)
#define ALL(v) v.begin(), v.end()
#define FIND(v, x) (binary_search(ALL(v), (x)))
#define SORT(v) sort(ALL(v))
#define RSORT(v)                                                               \
  sort(ALL(v));                                                                \
  reverse(ALL(v))
#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                                           \
  cerr << #v << ":";                                                           \
  for (int i = 0; i < v.size(); i++)                                           \
    cerr << " " << v[i];                                                       \
  cerr << endl
#define Yes(n) cout << ((n) ? "Yes" : "No") << endl
#define YES(n) cout << ((n) ? "YES" : "NO") << endl
#define pb push_back
#define fi first
#define se second
using namespace std;
template <class A> void pr(A a) { cout << (a) << endl; }
template <class A, class B> void pr(A a, B b) {
  cout << a << " ";
  pr(b);
}
template <class A, class B, class C> void pr(A a, B b, C c) {
  cout << a << " ";
  pr(b, c);
}
template <class A, class B, class C, class D> void pr(A a, B b, C c, D d) {
  cout << a << " ";
  pr(b, c, d);
}
template <class T> inline bool chmin(T &a, T b) {
  return a > b ? a = b, true : false;
}
template <class T> inline bool chmax(T &a, T b) {
  return a < b ? a = b, true : false;
}
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

int main(void) {
  string S;
  cin >> S;
  int N = S.size();
  vector<vector<ll>> dp(N + 1, vector<ll>(13, 0));
  dp[N][0] = 1;
  int mul = 1;
  RREP(i, N) {
    int c;
    if (S[i] == '?')
      c = -1;
    else
      c = S[i] - '0';
    REP(j, 10) {
      if (c != -1 && c != j)
        continue;
      REP(k, 13) { (dp[i][(j * mul + k) % 13] += dp[i + 1][k]) %= MOD; }
    }
    mul *= 10;
    mul %= MOD;
  }
  pr(dp[0][5]);
}

Fixed submission:
#include <bits/stdc++.h>
#include <numeric>
#include <vector>
#define PI 3.14159265358979323846
#define MAXINF (1e18L)
#define INF (1e9L)
#define EPS (1e-9)
#define MOD ((ll)(1e9 + 7))
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define Rep(i, sta, n) for (int i = sta; i < n; i++)
#define RREP(i, n) for (int i = int(n) - 1; i >= 0; --i)
#define ALL(v) v.begin(), v.end()
#define FIND(v, x) (binary_search(ALL(v), (x)))
#define SORT(v) sort(ALL(v))
#define RSORT(v)                                                               \
  sort(ALL(v));                                                                \
  reverse(ALL(v))
#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                                           \
  cerr << #v << ":";                                                           \
  for (int i = 0; i < v.size(); i++)                                           \
    cerr << " " << v[i];                                                       \
  cerr << endl
#define Yes(n) cout << ((n) ? "Yes" : "No") << endl
#define YES(n) cout << ((n) ? "YES" : "NO") << endl
#define pb push_back
#define fi first
#define se second
using namespace std;
template <class A> void pr(A a) { cout << (a) << endl; }
template <class A, class B> void pr(A a, B b) {
  cout << a << " ";
  pr(b);
}
template <class A, class B, class C> void pr(A a, B b, C c) {
  cout << a << " ";
  pr(b, c);
}
template <class A, class B, class C, class D> void pr(A a, B b, C c, D d) {
  cout << a << " ";
  pr(b, c, d);
}
template <class T> inline bool chmin(T &a, T b) {
  return a > b ? a = b, true : false;
}
template <class T> inline bool chmax(T &a, T b) {
  return a < b ? a = b, true : false;
}
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

int main(void) {
  string S;
  cin >> S;
  int N = S.size();
  vector<vector<ll>> dp(N + 1, vector<ll>(13, 0));
  dp[N][0] = 1;
  int mul = 1;
  RREP(i, N) {
    int c;
    if (S[i] == '?')
      c = -1;
    else
      c = S[i] - '0';
    REP(j, 10) {
      if (c != -1 && c != j)
        continue;
      REP(k, 13) { (dp[i][(j * mul + k) % 13] += dp[i + 1][k]) %= MOD; }
    }
    mul *= 10;
    mul %= 13;
  }
  pr(dp[0][5]);
}