Problem p02555 (C++) — buggy submission, verdict: Runtime Error

#include <bits/stdc++.h>
using namespace std;

template <typename A, typename B> string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string &s) { return '"' + s + '"'; }

string to_string(const char *s) { return to_string((string)s); }

string to_string(bool b) { return (b ? "true" : "false"); }

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N> string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A> string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

template <typename A, typename B> string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

#define fi first
#define se second
#define pb push_back
#define mod(n, k) ((((n) % (k)) + (k)) % (k))
#define forn(i, a, b) for (int i = a; i < b; i++)
#define forr(i, a, b) for (int i = a; i >= b; i--)
#define all(x) (x).begin(), (x).end()

typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef vector<int> vi;
typedef vector<ii> vii;

#define MAX 100000 + 10
#define MOD 1000000007

ll fac[MAX], caf[MAX]; // factorial e inverso

ll deg(ll x, ll d) {
  d %= MOD - 1;
  if (d < 0)
    d += MOD - 1;
  ll y = 1;
  while (d) {
    if (d & 1)
      y *= x, y %= MOD;
    x *= x, x %= MOD;
    d /= 2;
  }
  return y;
}
ll coeff(int n, int k) { return fac[n] * caf[k] % MOD * caf[n - k] % MOD; }

int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  fac[0] = caf[0] = 1;
  forn(i, 1, MAX) fac[i] = i * fac[i - 1] % MOD, caf[i] = deg(fac[i], -1);
  int S;
  cin >> S;
  ll res = 0;

  forn(i, 1, 2000) {
    int Sp = S - 3 * i;
    if (Sp < 0)
      break;
    ll add = coeff(i + Sp - 1, i - 1);
    res = ((res % MOD) + (add % MOD)) % MOD;
  }
  if (res < 0)
    res += MOD;
  cout << res << '\\n';

  return 0;
}
/*
__builtin_mul_overflow(x,y,&x)
-fsplit-stack
*/


Error: 0

Fixed submission:

#include <bits/stdc++.h>
using namespace std;

template <typename A, typename B> string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string &s) { return '"' + s + '"'; }

string to_string(const char *s) { return to_string((string)s); }

string to_string(bool b) { return (b ? "true" : "false"); }

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N> string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A> string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

template <typename A, typename B> string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

#define fi first
#define se second
#define pb push_back
#define mod(n, k) ((((n) % (k)) + (k)) % (k))
#define forn(i, a, b) for (int i = a; i < b; i++)
#define forr(i, a, b) for (int i = a; i >= b; i--)
#define all(x) (x).begin(), (x).end()

typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef vector<int> vi;
typedef vector<ii> vii;

const ll mod = 1e9 + 7;
const int maxn = 1000;
const int maxs = 2001;
ll memo[maxn][maxs];

ll dp(int pos, int s) {
  if (s < 0)
    return 0;
  if (pos <= 0) {
    return (s == 0);
  }
  ll &res = memo[pos][s];
  if (res != -1)
    return res;
  res = 0;
  forn(i, 3, 10) {
    res += dp(pos - 1, s - i);
    res %= mod;
  }
  return res;
}

int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  forn(i, 0, maxn) forn(j, 0, maxs) memo[i][j] = -1;
  int S;
  cin >> S;
  ll res = 0;
  forr(i, 1000, 1) {
    res += dp(i, S);
    // debug(i,dp(i,S));
    res %= mod;
  }
  if (res < 0)
    res += mod;
  cout << res << '\\n';

  return 0;
}
/*
__builtin_mul_overflow(x,y,&x)
-fsplit-stack
*/