Problem p03825 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#define ADD(a, b) a = (a + ll(b)) % mod
#define MUL(a, b) a = (a * ll(b)) % mod
#define MAX(a, b) a = max(a, b)
#define MIN(a, b) a = min(a, b)
#define rep(i, a, b) for (int i = int(a); i < int(b); i++)
#define rer(i, a, b) for (int i = int(a) - 1; i >= int(b); i--)
#define all(a) (a).begin(), (a).end()
#define sz(v) (int)(v).size()
#define pb push_back
#define sec second
#define fst first
#define debug(fmt, ...) Debug(__LINE__, ":", fmt, ##__VA_ARGS__)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<int, pi> ppi;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vl> mat;
typedef complex<double> comp;
void Debug() { cout << '\n'; }
template <class FIRST, class... REST> void Debug(FIRST arg, REST... rest) {
  cout << arg << " ";
  Debug(rest...);
}
template <class T> ostream &operator<<(ostream &out, const vector<T> &v) {
  out << "[";
  if (!v.empty()) {
    rep(i, 0, sz(v) - 1) out << v[i] << ", ";
    out << v.back();
  }
  out << "]";
  return out;
}
template <class S, class T>
ostream &operator<<(ostream &out, const pair<S, T> &v) {
  out << "(" << v.first << ", " << v.second << ")";
  return out;
}
const int MAX_N = 200010;
const int MAX_V = 100010;
const double eps = 1e-6;
const ll mod = 1000000007;
const int inf = 1 << 29;
const ll linf = 1LL << 60;
const double PI = 3.14159265358979323846;
///////////////////////////////////////////////////////////////////////////////////////////////////

ll dp[2][2010][2];
int N, M, K, T;

void solve() {
  cin >> N >> M >> K;
  int T = (N + M - 1) / (K - 1);

  int now = 0, nex = 1;
  dp[now][0][0] = 1;

  rep(i, 0, T) {
    memset(dp[nex], 0, sizeof(dp[nex]));
    rep(j, 0, M + 1) {
      rep(k, 0, 2) {
        if (!dp[now][j][k])
          continue;
        // debug(i, j, k, dp[now][j][k]);
        if (j == 0) {
          assert(k == 0);
          rep(cnt, 0, K) { ADD(dp[nex][j + cnt][0], dp[now][j][k]); }
          ADD(dp[nex][j + K][1], dp[now][j][k]);
        } else {
          if (k == 0) {
            rep(cnt, 0, K) { ADD(dp[nex][j + cnt][0], dp[now][j][k]); }
          } else {
            rep(cnt, 0, K - 1) { ADD(dp[nex][j + cnt][0], dp[now][j][k]); }
            ADD(dp[nex][j + K - 1][1], dp[now][j][k]);
          }
        }
      }
    }

    swap(now, nex);
  }
  cout << dp[now][M][0] << "\n";
}

int main() {
#ifndef LOCAL
  ios::sync_with_stdio(false);
  cin.tie(0);
#endif
  cout << fixed;
  cout.precision(20);
  srand((unsigned int)time(NULL));
#ifdef LOCAL
  // freopen("in.txt", "wt", stdout); //for tester
  freopen("in.txt", "rt", stdin);
#endif
  solve();
#ifdef LOCAL
  cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
#endif
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
#define ADD(a, b) a = (a + ll(b)) % mod
#define MUL(a, b) a = (a * ll(b)) % mod
#define MAX(a, b) a = max(a, b)
#define MIN(a, b) a = min(a, b)
#define rep(i, a, b) for (int i = int(a); i < int(b); i++)
#define rer(i, a, b) for (int i = int(a) - 1; i >= int(b); i--)
#define all(a) (a).begin(), (a).end()
#define sz(v) (int)(v).size()
#define pb push_back
#define sec second
#define fst first
#define debug(fmt, ...) Debug(__LINE__, ":", fmt, ##__VA_ARGS__)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<int, pi> ppi;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vl> mat;
typedef complex<double> comp;
void Debug() { cout << '\n'; }
template <class FIRST, class... REST> void Debug(FIRST arg, REST... rest) {
  cout << arg << " ";
  Debug(rest...);
}
template <class T> ostream &operator<<(ostream &out, const vector<T> &v) {
  out << "[";
  if (!v.empty()) {
    rep(i, 0, sz(v) - 1) out << v[i] << ", ";
    out << v.back();
  }
  out << "]";
  return out;
}
template <class S, class T>
ostream &operator<<(ostream &out, const pair<S, T> &v) {
  out << "(" << v.first << ", " << v.second << ")";
  return out;
}
const int MAX_N = 200010;
const int MAX_V = 100010;
const double eps = 1e-6;
const ll mod = 1000000007;
const int inf = 1 << 29;
const ll linf = 1LL << 60;
const double PI = 3.14159265358979323846;
///////////////////////////////////////////////////////////////////////////////////////////////////

ll dp[2][4010][2];
int N, M, K, T;

void solve() {
  cin >> N >> M >> K;
  int T = (N + M - 1) / (K - 1);

  int now = 0, nex = 1;
  dp[now][0][0] = 1;

  rep(i, 0, T) {
    memset(dp[nex], 0, sizeof(dp[nex]));
    rep(j, 0, M + 1) {
      rep(k, 0, 2) {
        if (!dp[now][j][k])
          continue;
        // debug(i, j, k, dp[now][j][k]);
        if (j == 0) {
          assert(k == 0);
          rep(cnt, 0, K) { ADD(dp[nex][j + cnt][0], dp[now][j][k]); }
          ADD(dp[nex][j + K][1], dp[now][j][k]);
        } else {
          if (k == 0) {
            rep(cnt, 0, K) { ADD(dp[nex][j + cnt][0], dp[now][j][k]); }
          } else {
            rep(cnt, 0, K - 1) { ADD(dp[nex][j + cnt][0], dp[now][j][k]); }
            ADD(dp[nex][j + K - 1][1], dp[now][j][k]);
          }
        }
      }
    }

    swap(now, nex);
  }
  cout << dp[now][M][0] << "\n";
}

int main() {
#ifndef LOCAL
  ios::sync_with_stdio(false);
  cin.tie(0);
#endif
  cout << fixed;
  cout.precision(20);
  srand((unsigned int)time(NULL));
#ifdef LOCAL
  // freopen("in.txt", "wt", stdout); //for tester
  freopen("in.txt", "rt", stdin);
#endif
  solve();
#ifdef LOCAL
  cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
#endif
  return 0;
}