Problem p02653 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <string>
#include <tuple>
#include <vector>
using namespace std;
typedef long long int LL;
typedef pair<int, int> P;
typedef pair<LL, int> LP;
const int INF = 1 << 30;
const LL MAX = 1e9 + 7;

void array_show(int *array, int array_n, char middle = ' ') {
  for (int i = 0; i < array_n; i++)
    printf("%d%c", array[i], (i != array_n - 1 ? middle : '\n'));
}
void array_show(LL *array, int array_n, char middle = ' ') {
  for (int i = 0; i < array_n; i++)
    printf("%lld%c", array[i], (i != array_n - 1 ? middle : '\n'));
}
void array_show(vector<int> &vec_s, int vec_n = -1, char middle = ' ') {
  if (vec_n == -1)
    vec_n = vec_s.size();
  for (int i = 0; i < vec_n; i++)
    printf("%d%c", vec_s[i], (i != vec_n - 1 ? middle : '\n'));
}
void array_show(vector<LL> &vec_s, int vec_n = -1, char middle = ' ') {
  if (vec_n == -1)
    vec_n = vec_s.size();
  for (int i = 0; i < vec_n; i++)
    printf("%lld%c", vec_s[i], (i != vec_n - 1 ? middle : '\n'));
}

LL dp[3300][3300];
LL t[3300];
LL t2[3300];

long long int pow_mod(long long int p_a, long long int p_n,
                      long long int p_p = 1e9 + 7) {
  // p_a^p_n mod p_p
  long long int p_b = 1, p_t = 1;
  for (; p_b <= p_n; p_b <<= 1)
    ;
  for (p_b >>= 1; p_b > 0; p_b >>= 1) {
    p_t *= p_t;
    if (p_t >= p_p)
      p_t %= p_p;
    if (p_n & p_b)
      p_t *= p_a;
    if (p_t >= p_p)
      p_t %= p_p;
  }
  return p_t;
}

int main() {
  int n, m;
  int i, j, k;
  LL a, b, c;
  LL x, y;
  LL s[10] = {0};
  cin >> n;
  cin >> x >> y;
  if (x < y)
    swap(x, y);

  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (i = 0; i < x; i++) {
    dp[i + 1][0] = dp[i][0];
    a = 0;
    for (j = 0; j < x; j++) {
      dp[i + 1][j + 1] = dp[i][j];
      if (j >= y)
        a += dp[i][j];
    }
    a %= MAX;
    dp[i + 1][0] += a;
    if (dp[i + 1][0] >= MAX)
      dp[i + 1][0] %= MAX;
  }
  for (i = 0; i <= x; i++) {
    t[i] = dp[i][0];
  }

  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (i = 0; i <= n; i++) {
    if (i + 1 < x) {
      dp[i + 1][0] += t[i + 1];
      dp[i + 1][0] %= MAX;
    }
    for (j = 0; j < y; j++) {
      dp[i + 1][j + 1] = dp[i][j];
      if (j)
        t2[i] += dp[i][j];
    }
    t2[i] %= MAX;
    a = 0;
    for (j = 0; j < x - 1; j++) {
      if (i - j < 0)
        break;
      a += t2[i - j] * t[j];
      if (a >= MAX)
        a %= MAX;
    }
    dp[i + 1][0] += a;
    dp[i + 1][0] %= MAX;
  }
  for (i = 1; i < y; i++) {
    s[2] += dp[n][i];
  }
  for (j = 1; j < x; j++) {
    if (n - j < 0)
      break;
    s[2] += t2[n - j] * t[j];
    if (s[2] >= MAX)
      s[2] %= MAX;
  }
  s[2] %= MAX;
  s[0] = pow_mod(2, n) - s[2];
  if (s[0] < 0)
    s[0] += MAX;
  cout << s[0] % MAX << endl;
}

Fixed submission:
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <string>
#include <tuple>
#include <vector>
using namespace std;
typedef long long int LL;
typedef pair<int, int> P;
typedef pair<LL, int> LP;
const int INF = 1 << 30;
const LL MAX = 1e9 + 7;

void array_show(int *array, int array_n, char middle = ' ') {
  for (int i = 0; i < array_n; i++)
    printf("%d%c", array[i], (i != array_n - 1 ? middle : '\n'));
}
void array_show(LL *array, int array_n, char middle = ' ') {
  for (int i = 0; i < array_n; i++)
    printf("%lld%c", array[i], (i != array_n - 1 ? middle : '\n'));
}
void array_show(vector<int> &vec_s, int vec_n = -1, char middle = ' ') {
  if (vec_n == -1)
    vec_n = vec_s.size();
  for (int i = 0; i < vec_n; i++)
    printf("%d%c", vec_s[i], (i != vec_n - 1 ? middle : '\n'));
}
void array_show(vector<LL> &vec_s, int vec_n = -1, char middle = ' ') {
  if (vec_n == -1)
    vec_n = vec_s.size();
  for (int i = 0; i < vec_n; i++)
    printf("%lld%c", vec_s[i], (i != vec_n - 1 ? middle : '\n'));
}

LL dp[5300][5300];
LL t[5300];
LL t2[5300];

long long int pow_mod(long long int p_a, long long int p_n,
                      long long int p_p = 1e9 + 7) {
  // p_a^p_n mod p_p
  long long int p_b = 1, p_t = 1;
  for (; p_b <= p_n; p_b <<= 1)
    ;
  for (p_b >>= 1; p_b > 0; p_b >>= 1) {
    p_t *= p_t;
    if (p_t >= p_p)
      p_t %= p_p;
    if (p_n & p_b)
      p_t *= p_a;
    if (p_t >= p_p)
      p_t %= p_p;
  }
  return p_t;
}

int main() {
  int n, m;
  int i, j, k;
  LL a, b, c;
  LL x, y;
  LL s[10] = {0};
  cin >> n;
  cin >> x >> y;
  if (x < y)
    swap(x, y);

  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (i = 0; i < x; i++) {
    dp[i + 1][0] = dp[i][0];
    a = 0;
    for (j = 0; j < x; j++) {
      dp[i + 1][j + 1] = dp[i][j];
      if (j >= y)
        a += dp[i][j];
    }
    a %= MAX;
    dp[i + 1][0] += a;
    if (dp[i + 1][0] >= MAX)
      dp[i + 1][0] %= MAX;
  }
  for (i = 0; i <= x; i++) {
    t[i] = dp[i][0];
  }

  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (i = 0; i <= n; i++) {
    if (i + 1 < x) {
      dp[i + 1][0] += t[i + 1];
      dp[i + 1][0] %= MAX;
    }
    for (j = 0; j < y; j++) {
      dp[i + 1][j + 1] = dp[i][j];
      if (j)
        t2[i] += dp[i][j];
    }
    t2[i] %= MAX;
    a = 0;
    for (j = 0; j < x - 1; j++) {
      if (i - j < 0)
        break;
      a += t2[i - j] * t[j];
      if (a >= MAX)
        a %= MAX;
    }
    dp[i + 1][0] += a;
    dp[i + 1][0] %= MAX;
  }
  for (i = 1; i < y; i++) {
    s[2] += dp[n][i];
  }
  for (j = 1; j < x; j++) {
    if (n - j < 0)
      break;
    s[2] += t2[n - j] * t[j];
    if (s[2] >= MAX)
      s[2] %= MAX;
  }
  s[2] %= MAX;
  s[0] = pow_mod(2, n) - s[2];
  if (s[0] < 0)
    s[0] += MAX;
  cout << s[0] % MAX << endl;
}