Problem p04028 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <bitset>
#include <complex>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string.h>
#include <string>
#include <utility>
#include <vector>
using namespace std;

#define int long long
#define reps(i, s, n) for (int(i) = (s); (i) < (n); ++(i))
#define rep(i, n) reps(i, 0, n)
#define rept(i, n) rep(i, (n) + 1)
#define repst(i, s, n) reps(i, s, (n) + 1)
#define reprt(i, n, t) for (int(i) = (n); (i) >= (t); --(i))
#define repr(i, n) reprt(i, n, 0)
#define each(i, v) for (auto &(i) : (v))
#define eachr(i, v) for (auto &(i) = (v).rbegin(); (i) != (v).rend(); (i)++)
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define tmax(x, y, z) max(x, max(y, z))
#define tmin(x, y, z) min(x, min(y, z))
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define ln '\n'
#define bln(i, n) (((i) == (n)-1) ? '\n' : ' ')
#define dbg(x) cout << #x " = " << (x) << ln << flush
#define dbga(x, n)                                                             \
  {                                                                            \
    cout << #x " : ";                                                          \
    for (int(i) = 0; i < (n); ++i) {                                           \
      cout << ((x)[i]) << (i == ((n)-1) ? '\n' : ' ') << flush;                \
    }                                                                          \
  }
#define zero(a) memset(a, 0, sizeof(a))
#define unq(a) sort(all(a)), a.erase(unique(all(a)), a.end())

// typedef complex<double> P;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<string> vst;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<vector<int>> mat;

const ll inf = (ll)1e9 + 10;
const ll linf = (ll)1e18 + 10;
const ll mod = (ll)(1e9 + 7);
const int dx[] = {0, 1, 0, -1};
const int dy[] = {1, 0, -1, 0};
const int ddx[] = {0, 1, 1, 1, 0, -1, -1, -1};
const int ddy[] = {1, 1, 0, -1, -1, -1, 0, 1};
const double eps = 1e-10;

ll mop(ll a, ll b, ll m = mod) {
  ll r = 1;
  a %= m;
  for (; b; b >>= 1) {
    if (b & 1)
      r = r * a % m;
    a = a * a % m;
  }
  return r;
}
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
bool ool(int x, int y, int h, int w) {
  return ((x < 0) || (h <= x) || (y < 0) || (w <= y));
}
bool deq(double a, double b) { return abs(a - b) < eps; }

struct oreno_initializer {
  oreno_initializer() {
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
} oreno_initializer;

int n, m, dp[5050][5050];
string s;

signed main() {
  cin >> n >> s;
  m = s.size();
  dp[0][0] = 1;
  rep(i, n) rep(j, 5050) {
    if (j)
      (dp[i + 1][j - 1] += dp[i][j]) %= mod;
    else
      (dp[i + 1][j] += dp[i][j]) %= mod;
    (dp[i + 1][j + 1] += dp[i][j] * 2) %= mod;
  }
  cout << dp[n][m] * mop(mop(2, m), mod - 2) % mod << endl;
}

Fixed submission:
#include <algorithm>
#include <bitset>
#include <complex>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string.h>
#include <string>
#include <utility>
#include <vector>
using namespace std;

#define int long long
#define reps(i, s, n) for (int(i) = (s); (i) < (n); ++(i))
#define rep(i, n) reps(i, 0, n)
#define rept(i, n) rep(i, (n) + 1)
#define repst(i, s, n) reps(i, s, (n) + 1)
#define reprt(i, n, t) for (int(i) = (n); (i) >= (t); --(i))
#define repr(i, n) reprt(i, n, 0)
#define each(i, v) for (auto &(i) : (v))
#define eachr(i, v) for (auto &(i) = (v).rbegin(); (i) != (v).rend(); (i)++)
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define tmax(x, y, z) max(x, max(y, z))
#define tmin(x, y, z) min(x, min(y, z))
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define ln '\n'
#define bln(i, n) (((i) == (n)-1) ? '\n' : ' ')
#define dbg(x) cout << #x " = " << (x) << ln << flush
#define dbga(x, n)                                                             \
  {                                                                            \
    cout << #x " : ";                                                          \
    for (int(i) = 0; i < (n); ++i) {                                           \
      cout << ((x)[i]) << (i == ((n)-1) ? '\n' : ' ') << flush;                \
    }                                                                          \
  }
#define zero(a) memset(a, 0, sizeof(a))
#define unq(a) sort(all(a)), a.erase(unique(all(a)), a.end())

// typedef complex<double> P;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<string> vst;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<vector<int>> mat;

const ll inf = (ll)1e9 + 10;
const ll linf = (ll)1e18 + 10;
const ll mod = (ll)(1e9 + 7);
const int dx[] = {0, 1, 0, -1};
const int dy[] = {1, 0, -1, 0};
const int ddx[] = {0, 1, 1, 1, 0, -1, -1, -1};
const int ddy[] = {1, 1, 0, -1, -1, -1, 0, 1};
const double eps = 1e-10;

ll mop(ll a, ll b, ll m = mod) {
  ll r = 1;
  a %= m;
  for (; b; b >>= 1) {
    if (b & 1)
      r = r * a % m;
    a = a * a % m;
  }
  return r;
}
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
bool ool(int x, int y, int h, int w) {
  return ((x < 0) || (h <= x) || (y < 0) || (w <= y));
}
bool deq(double a, double b) { return abs(a - b) < eps; }

struct oreno_initializer {
  oreno_initializer() {
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
} oreno_initializer;

int n, m, dp[5050][5050];
string s;

signed main() {
  cin >> n >> s;
  m = s.size();
  dp[0][0] = 1;
  rep(i, n) rep(j, 5040) {
    if (j)
      (dp[i + 1][j - 1] += dp[i][j]) %= mod;
    else
      (dp[i + 1][j] += dp[i][j]) %= mod;
    (dp[i + 1][j + 1] += dp[i][j] * 2) %= mod;
  }
  cout << dp[n][m] * mop(mop(2, m), mod - 2) % mod << endl;
}