Problem p03825 (C++)

Buggy submission (status: Runtime Error):
// Copyright (C) 2017 __debug.

// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; version 3

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program; If not, see <http://www.gnu.org/licenses/>.

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/priority_queue.hpp>

#define x first
#define y second
#define MP std::make_pair
#define SZ(x) ((int)(x).size())
#define ALL(x) (x).begin(), (x).end()
#define DEBUG(...) fprintf(stderr, __VA_ARGS__)
#ifdef __linux__
#define getchar getchar_unlocked
#define putchar putchar_unlocked
#endif

using std::pair;
using std::string;
using std::vector;

typedef long long LL;
typedef pair<int, int> Pii;

const int oo = 0x3f3f3f3f;

template <typename T> inline bool chkmax(T &a, T b) {
  return a < b ? a = b, true : false;
}
template <typename T> inline bool chkmin(T &a, T b) {
  return b < a ? a = b, true : false;
}
string procStatus() {
  std::ifstream t("/proc/self/status");
  return string(std::istreambuf_iterator<char>(t),
                std::istreambuf_iterator<char>());
}
template <typename T> T read(T &x) {
  int f = 1;
  char ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    f = (ch == '-' ? -1 : 1);
  for (x = 0; isdigit(ch); ch = getchar())
    x = 10 * x + ch - '0';
  return x *= f;
}
template <typename T> void write(T x) {
  if (x == 0) {
    putchar('0');
    return;
  }
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  static char s[20];
  int top = 0;
  for (; x; x /= 10)
    s[++top] = x % 10 + '0';
  while (top)
    putchar(s[top--]);
}
// EOT

const int MAXN = 2e3 + 5;
const int MOD = 1e9 + 7;

int N, M, K;

void input() {
  read(M);
  read(N);
  read(K);
}

void solve() {
  static int dp[MAXN][MAXN][2];
  int t = (N + M - 1) / (K - 1);

  dp[0][0][0] = 1;
  for (int i = 0; i < t; ++i) {
    for (int x = 0; x <= N; ++x) {
      for (int j = 0; j <= 1; ++j) {
        if (!dp[i][x][j])
          continue;
        int y = i * (K - 1) - x;
        // printf("%d %d %d %d: %d\n", i, x, y, j, dp[i][x][j]);
        for (int z = 0; z < K; ++z) {
          int x0 = x + z, y0 = y + K - 1 - z;
          if (x0 <= N && y0 <= M - 1)
            (dp[i + 1][x0][!!z] += dp[i][x][j]) %= MOD;
        }
      }
    }
  }

  int ans = 0;
  for (int i = 0; i <= t; ++i) {
    for (int x = 0; x <= N && i * (K - 1) - x >= 0; ++x) {
      int y = i * (K - 1) - x;
      if (x % (K - 1) == N % (K - 1) && y % (K - 1) == (M - 1) % (K - 1)) {
        // printf("%d %d %d\n", x, y, dp[i][x][1]);
        (ans += dp[i][x][1]) %= MOD;
      }
    }
  }

  printf("%d\n", ans);
}

int main() {
#ifdef __DEBUG
  freopen("E.in", "r", stdin);
  freopen("E.out", "w", stdout);
#endif

  input();
  solve();

  return 0;
}

// 人生如寄，何事辛苦怨斜晖。
//     -- 朱熹《水调歌头·隐括杜牧之齐山诗》


Fixed submission:
// Copyright (C) 2017 __debug.

// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; version 3

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program; If not, see <http://www.gnu.org/licenses/>.

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/priority_queue.hpp>

#define x first
#define y second
#define MP std::make_pair
#define SZ(x) ((int)(x).size())
#define ALL(x) (x).begin(), (x).end()
#define DEBUG(...) fprintf(stderr, __VA_ARGS__)
#ifdef __linux__
#define getchar getchar_unlocked
#define putchar putchar_unlocked
#endif

using std::pair;
using std::string;
using std::vector;

typedef long long LL;
typedef pair<int, int> Pii;

const int oo = 0x3f3f3f3f;

template <typename T> inline bool chkmax(T &a, T b) {
  return a < b ? a = b, true : false;
}
template <typename T> inline bool chkmin(T &a, T b) {
  return b < a ? a = b, true : false;
}
string procStatus() {
  std::ifstream t("/proc/self/status");
  return string(std::istreambuf_iterator<char>(t),
                std::istreambuf_iterator<char>());
}
template <typename T> T read(T &x) {
  int f = 1;
  char ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    f = (ch == '-' ? -1 : 1);
  for (x = 0; isdigit(ch); ch = getchar())
    x = 10 * x + ch - '0';
  return x *= f;
}
template <typename T> void write(T x) {
  if (x == 0) {
    putchar('0');
    return;
  }
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  static char s[20];
  int top = 0;
  for (; x; x /= 10)
    s[++top] = x % 10 + '0';
  while (top)
    putchar(s[top--]);
}
// EOT

const int MAXN = 4e3 + 5;
const int MOD = 1e9 + 7;

int N, M, K;

void input() {
  read(M);
  read(N);
  read(K);
}

void solve() {
  static int dp[MAXN][MAXN][2];
  int t = (N + M - 1) / (K - 1);

  dp[0][0][0] = 1;
  for (int i = 0; i < t; ++i) {
    for (int x = 0; x <= N; ++x) {
      for (int j = 0; j <= 1; ++j) {
        if (!dp[i][x][j])
          continue;
        int y = i * (K - 1) - x;
        // printf("%d %d %d %d: %d\n", i, x, y, j, dp[i][x][j]);
        for (int z = 0; z < K; ++z) {
          int x0 = x + z, y0 = y + K - 1 - z;
          if (x0 <= N && y0 <= M - 1)
            (dp[i + 1][x0][!!z] += dp[i][x][j]) %= MOD;
        }
      }
    }
  }

  int ans = 0;
  for (int i = 0; i <= t; ++i) {
    for (int x = 0; x <= N && i * (K - 1) - x >= 0; ++x) {
      int y = i * (K - 1) - x;
      if (x % (K - 1) == N % (K - 1) && y % (K - 1) == (M - 1) % (K - 1)) {
        // printf("%d %d %d\n", x, y, dp[i][x][1]);
        (ans += dp[i][x][1]) %= MOD;
      }
    }
  }

  printf("%d\n", ans);
}

int main() {
#ifdef __DEBUG
  freopen("E.in", "r", stdin);
  freopen("E.out", "w", stdout);
#endif

  input();
  solve();

  return 0;
}

// 人生如寄，何事辛苦怨斜晖。
//     -- 朱熹《水调歌头·隐括杜牧之齐山诗》