Problem p03825 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#define MP make_pair
#define PB push_back
#define int long long
#define st first
#define nd second
#define rd third
#define FOR(i, a, b) for (int i = (a); i <= (b); ++i)
#define RE(i, n) FOR(i, 1, n)
#define FORD(i, a, b) for (int i = (a); i >= (b); --i)
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define VAR(v, i) __typeof(i) v = (i)
#define FORE(i, c) for (VAR(i, (c).begin()); i != (c).end(); ++i)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
using namespace std;
template <typename TH> void _dbg(const char *sdbg, TH h) {
  cerr << sdbg << "=" << h << "\n";
}
template <typename TH, typename... TA>
void _dbg(const char *sdbg, TH h, TA... t) {
  while (*sdbg != ',')
    cerr << *sdbg++;
  cerr << "=" << h << ",";
  _dbg(sdbg + 1, t...);
}
#ifdef LOCAL
#define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
#define debugv(x)                                                              \
  {                                                                            \
    {                                                                          \
      cerr << #x << " = ";                                                     \
      FORE(itt, (x)) cerr << *itt << ", ";                                     \
      cerr << "\n";                                                            \
    }                                                                          \
  }
#else
#define debug(...) (__VA_ARGS__)
#define debugv(x)
#define cerr                                                                   \
  if (0)                                                                       \
  cout
#endif
#define next ____next
#define prev ____prev
#define left ____left
#define hash ____hash
typedef long long ll;
typedef long double LD;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<ll> VLL;
typedef vector<pair<int, int>> VPII;
typedef vector<pair<ll, ll>> VPLL;

template <class C> void mini(C &a4, C b4) { a4 = min(a4, b4); }
template <class C> void maxi(C &a4, C b4) { a4 = max(a4, b4); }
template <class T1, class T2>
ostream &operator<<(ostream &out, pair<T1, T2> pair) {
  return out << "(" << pair.first << ", " << pair.second << ")";
}
template <class A, class B, class C> struct Triple {
  A first;
  B second;
  C third;
  bool operator<(const Triple &t) const {
    if (st != t.st)
      return st < t.st;
    if (nd != t.nd)
      return nd < t.nd;
    return rd < t.rd;
  }
};
template <class T> void ResizeVec(T &, vector<int>) {}
template <class T> void ResizeVec(vector<T> &vec, vector<int> sz) {
  vec.resize(sz[0]);
  sz.erase(sz.begin());
  if (sz.empty()) {
    return;
  }
  for (T &v : vec) {
    ResizeVec(v, sz);
  }
}
typedef Triple<int, int, int> TIII;
template <class A, class B, class C>
ostream &operator<<(ostream &out, Triple<A, B, C> t) {
  return out << "(" << t.st << ", " << t.nd << ", " << t.rd << ")";
}
template <class T> ostream &operator<<(ostream &out, vector<T> vec) {
  out << "(";
  for (auto &v : vec)
    out << v << ", ";
  return out << ")";
}

const int P = 1e9 + 7;
const int N = 2e3 + 5;
int dp[N][N];
int32_t main() {

  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(10);
  cerr << fixed << setprecision(10);
  cin.tie(0);
  // double beg_clock = 1.0 * clock() / CLOCKS_PER_SEC;

  int n, m, k;
  cin >> n >> m >> k;
  int l = (n + m - 1) / (k - 1);
  dp[0][0] = 1;
  RE(d, l) {
    REP(here, k) {
      FOR(prev_sum, 0, m) {
        int new_sum = prev_sum + here;
        dp[d][new_sum] = (dp[d][new_sum] + dp[d - 1][prev_sum]) % P;
      }
    }
  }
  int res = 0;
  for (int S = m; S > 0; S -= k - 1) {
    int lacks = (m - S) / (k - 1);
    res += dp[l - lacks][S];
    res %= P;
  }
  cout << res << endl;

  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
#define MP make_pair
#define PB push_back
#define int long long
#define st first
#define nd second
#define rd third
#define FOR(i, a, b) for (int i = (a); i <= (b); ++i)
#define RE(i, n) FOR(i, 1, n)
#define FORD(i, a, b) for (int i = (a); i >= (b); --i)
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define VAR(v, i) __typeof(i) v = (i)
#define FORE(i, c) for (VAR(i, (c).begin()); i != (c).end(); ++i)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
using namespace std;
template <typename TH> void _dbg(const char *sdbg, TH h) {
  cerr << sdbg << "=" << h << "\n";
}
template <typename TH, typename... TA>
void _dbg(const char *sdbg, TH h, TA... t) {
  while (*sdbg != ',')
    cerr << *sdbg++;
  cerr << "=" << h << ",";
  _dbg(sdbg + 1, t...);
}
#ifdef LOCAL
#define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
#define debugv(x)                                                              \
  {                                                                            \
    {                                                                          \
      cerr << #x << " = ";                                                     \
      FORE(itt, (x)) cerr << *itt << ", ";                                     \
      cerr << "\n";                                                            \
    }                                                                          \
  }
#else
#define debug(...) (__VA_ARGS__)
#define debugv(x)
#define cerr                                                                   \
  if (0)                                                                       \
  cout
#endif
#define next ____next
#define prev ____prev
#define left ____left
#define hash ____hash
typedef long long ll;
typedef long double LD;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<ll> VLL;
typedef vector<pair<int, int>> VPII;
typedef vector<pair<ll, ll>> VPLL;

template <class C> void mini(C &a4, C b4) { a4 = min(a4, b4); }
template <class C> void maxi(C &a4, C b4) { a4 = max(a4, b4); }
template <class T1, class T2>
ostream &operator<<(ostream &out, pair<T1, T2> pair) {
  return out << "(" << pair.first << ", " << pair.second << ")";
}
template <class A, class B, class C> struct Triple {
  A first;
  B second;
  C third;
  bool operator<(const Triple &t) const {
    if (st != t.st)
      return st < t.st;
    if (nd != t.nd)
      return nd < t.nd;
    return rd < t.rd;
  }
};
template <class T> void ResizeVec(T &, vector<int>) {}
template <class T> void ResizeVec(vector<T> &vec, vector<int> sz) {
  vec.resize(sz[0]);
  sz.erase(sz.begin());
  if (sz.empty()) {
    return;
  }
  for (T &v : vec) {
    ResizeVec(v, sz);
  }
}
typedef Triple<int, int, int> TIII;
template <class A, class B, class C>
ostream &operator<<(ostream &out, Triple<A, B, C> t) {
  return out << "(" << t.st << ", " << t.nd << ", " << t.rd << ")";
}
template <class T> ostream &operator<<(ostream &out, vector<T> vec) {
  out << "(";
  for (auto &v : vec)
    out << v << ", ";
  return out << ")";
}

const int P = 1e9 + 7;
const int N = 4e3 + 5;
int dp[N][N];
int32_t main() {

  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(10);
  cerr << fixed << setprecision(10);
  cin.tie(0);
  // double beg_clock = 1.0 * clock() / CLOCKS_PER_SEC;

  int n, m, k;
  cin >> n >> m >> k;
  int l = (n + m - 1) / (k - 1);
  dp[0][0] = 1;
  RE(d, l) {
    REP(here, k) {
      FOR(prev_sum, 0, m) {
        int new_sum = prev_sum + here;
        dp[d][new_sum] = (dp[d][new_sum] + dp[d - 1][prev_sum]) % P;
      }
    }
  }
  int res = 0;
  for (int S = m; S > 0; S -= k - 1) {
    int lacks = (m - S) / (k - 1);
    res += dp[l - lacks][S];
    res %= P;
  }
  cout << res << endl;

  return 0;
}