Problem p04028 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#pragma GCC optimize("O2")
#pragma GCC optimize("unroll-loops")
// #pragma GCC optimize("no-stack-protector,fast-math")

using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<pii, int> piii;
typedef pair<ll, ll> pll;
#define debug(x) cerr << #x << '=' << (x) << endl;
#define debugp(x)                                                              \
  cerr << #x << "= {" << (x.first) << ", " << (x.second) << "}" << endl;
#define debug2(x, y)                                                           \
  cerr << "{" << #x << ", " << #y << "} = {" << (x) << ", " << (y) << "}"      \
       << endl;
#define debugv(v)                                                              \
  cerr << #v << " : ";                                                         \
  for (auto x : v)                                                             \
    cerr << x << ' ';                                                          \
  cerr << endl;
#define all(x) x.begin(), x.end()
#define pb push_back
#define kill(x) return cout << x << '\n', 0;

const ld eps = 1e-7;
const int inf = 1000000010;
const ll INF = 10000000000000010LL;
const int mod = 1000000007;
const int MAXN = 5010, LOG = 20;

ll n, m, k, u, v, x, y, t, a, b, ans;
ll dp[MAXN][MAXN];
string shit;

ll powmod(ll a, ll b) {
  ll res = 1;
  for (; b; b >>= 1, a = a * a % mod)
    if (b & 1)
      res = res * a % mod;
  return res;
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  // freopen("input.txt", "r", stdin);
  // freopen("output.txt", "w", stdout);
  dp[0][0] = 1;
  for (int i = 1; i < MAXN; i++) {
    dp[i][0] = (dp[i - 1][0] + dp[i - 1][1]) % mod;
    for (int j = 1; j <= i; j++)
      dp[i][j] = (dp[i - 1][j - 1] * 2 + dp[i - 1][j + 1]) % mod;
  }

  cin >> n >> shit;
  m = shit.size();
  ans = dp[n][m];
  ans = ans * powmod(2, mod - 1 - m) % mod;
  cout << ans << "\n";

  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
#pragma GCC optimize("O2")
#pragma GCC optimize("unroll-loops")
// #pragma GCC optimize("no-stack-protector,fast-math")

using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<pii, int> piii;
typedef pair<ll, ll> pll;
#define debug(x) cerr << #x << '=' << (x) << endl;
#define debugp(x)                                                              \
  cerr << #x << "= {" << (x.first) << ", " << (x.second) << "}" << endl;
#define debug2(x, y)                                                           \
  cerr << "{" << #x << ", " << #y << "} = {" << (x) << ", " << (y) << "}"      \
       << endl;
#define debugv(v)                                                              \
  cerr << #v << " : ";                                                         \
  for (auto x : v)                                                             \
    cerr << x << ' ';                                                          \
  cerr << endl;
#define all(x) x.begin(), x.end()
#define pb push_back
#define kill(x) return cout << x << '\n', 0;

const ld eps = 1e-7;
const int inf = 1000000010;
const ll INF = 10000000000000010LL;
const int mod = 1000000007;
const int MAXN = 5010, LOG = 20;

ll n, m, k, u, v, x, y, t, a, b, ans;
ll dp[MAXN][MAXN];
string shit;

ll powmod(ll a, ll b) {
  ll res = 1;
  for (; b; b >>= 1, a = a * a % mod)
    if (b & 1)
      res = res * a % mod;
  return res;
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  // freopen("input.txt", "r", stdin);
  // freopen("output.txt", "w", stdout);
  dp[0][0] = 1;
  for (int i = 1; i + 1 < MAXN; i++) {
    dp[i][0] = (dp[i - 1][0] + dp[i - 1][1]) % mod;
    for (int j = 1; j <= i; j++)
      dp[i][j] = (dp[i - 1][j - 1] * 2 + dp[i - 1][j + 1]) % mod;
  }

  cin >> n >> shit;
  m = shit.size();
  ans = dp[n][m];
  ans = ans * powmod(2, mod - 1 - m) % mod;
  cout << ans << "\n";

  return 0;
}