Problem p02668 (C++) — buggy submission, verdict: Time Limit Exceeded

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

using namespace std;
using namespace __gnu_pbds;

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define fbo find_by_order
#define ook order_of_key

typedef long long ll;
typedef pair<ll, ll> ii;
typedef vector<int> vi;
typedef long double ld;
typedef tree<ll, null_type, less<ll>, rb_tree_tag,
             tree_order_statistics_node_update>
    pbds;

vector<int> fact;
vector<int> ifact;
vector<int> inv;
vector<int> pow2;
const int MOD = (1e9 + 7);
int add(int a, int b) {
  a += b;
  while (a >= MOD)
    a -= MOD;
  return a;
}
void radd(int &a, int b) { a = add(a, b); }
int mult(int a, int b) { return (a * 1LL * b) % MOD; }
void rmult(int &a, int b) { a = mult(a, b); }
int modpow(int a, int b) {
  int r = 1;
  while (b) {
    if (b & 1)
      r = mult(r, a);
    a = mult(a, a);
    b >>= 1;
  }
  return r;
}
int choose(int a, int b) {
  if (a < b)
    return 0;
  if (b == 0)
    return 1;
  if (a == b)
    return 1;
  return mult(fact[a], mult(ifact[b], ifact[a - b]));
}
int inverse(int a) { return modpow(a, MOD - 2); }
void init(int _n) {
  fact.clear();
  ifact.clear();
  inv.clear();
  pow2.clear();
  fact.resize(_n + 1);
  ifact.resize(_n + 1);
  inv.resize(_n + 1);
  pow2.resize(_n + 1);
  pow2[0] = 1;
  ifact[0] = 1;
  fact[0] = 1;
  for (int i = 1; i <= _n; i++) {
    pow2[i] = add(pow2[i - 1], pow2[i - 1]);
    fact[i] = mult(fact[i - 1], i);
    // ifact[i]=mult(ifact[i-1],inv[i]);
  }
  ifact[_n] = inverse(fact[_n]);
  for (int i = _n - 1; i >= 1; i--) {
    ifact[i] = mult(ifact[i + 1], i + 1);
  }
  for (int i = 1; i <= _n; i++) {
    inv[i] = mult(fact[i - 1], ifact[i]);
  }
}
int ipow2[5555];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  init(5555);
  for (int i = 0; i < 5011; i++)
    ipow2[i] = inverse(pow2[i]);
  int n, m;
  cin >> n >> m;
  vi old(m + 1, 0);
  old[m] = 1;
  for (int z = 1; z <= n; z++) {
    vi nw(m + 1, 0);
    vi suf(m + 2, 0);
    for (int i = m; i >= 1; i--) {
      suf[i] = add(suf[i + 1], mult(pow2[i], old[i]));
    }
    for (int i = 1; i <= m; i++) {
      nw[i] = add(nw[i], mult(old[i], i + 1));
      nw[i] = add(nw[i], mult(mult(i, ipow2[i + 1]), suf[i + 1]));
    }
    old = nw;
  }
  int ans = 0;
  for (int i = 1; i <= m; i++)
    radd(ans, old[i]);
  cout << ans << '\\n';
}


Error: TLE

Fixed submission:

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

using namespace std;
using namespace __gnu_pbds;

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define fbo find_by_order
#define ook order_of_key

typedef long long ll;
typedef pair<ll, ll> ii;
typedef vector<int> vi;
typedef long double ld;
typedef tree<ll, null_type, less<ll>, rb_tree_tag,
             tree_order_statistics_node_update>
    pbds;

vector<int> fact;
vector<int> ifact;
vector<int> inv;
vector<int> pow2;
const int MOD = (1e9 + 7);
int add(int a, int b) {
  a += b;
  while (a >= MOD)
    a -= MOD;
  return a;
}
void radd(int &a, int b) { a = add(a, b); }
int mult(int a, int b) { return (a * 1LL * b) % MOD; }
void rmult(int &a, int b) { a = mult(a, b); }
int modpow(int a, int b) {
  int r = 1;
  while (b) {
    if (b & 1)
      r = mult(r, a);
    a = mult(a, a);
    b >>= 1;
  }
  return r;
}
int choose(int a, int b) {
  if (a < b)
    return 0;
  if (b == 0)
    return 1;
  if (a == b)
    return 1;
  return mult(fact[a], mult(ifact[b], ifact[a - b]));
}
int inverse(int a) { return modpow(a, MOD - 2); }
void init(int _n) {
  fact.clear();
  ifact.clear();
  inv.clear();
  pow2.clear();
  fact.resize(_n + 1);
  ifact.resize(_n + 1);
  inv.resize(_n + 1);
  pow2.resize(_n + 1);
  pow2[0] = 1;
  ifact[0] = 1;
  fact[0] = 1;
  for (int i = 1; i <= _n; i++) {
    pow2[i] = add(pow2[i - 1], pow2[i - 1]);
    fact[i] = mult(fact[i - 1], i);
    // ifact[i]=mult(ifact[i-1],inv[i]);
  }
  ifact[_n] = inverse(fact[_n]);
  for (int i = _n - 1; i >= 1; i--) {
    ifact[i] = mult(ifact[i + 1], i + 1);
  }
  for (int i = 1; i <= _n; i++) {
    inv[i] = mult(fact[i - 1], ifact[i]);
  }
}

int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  init(5555);
  int n, m;
  cin >> n >> m;
  vi old(m + 1, 0);
  old[m] = 1;
  for (int z = 1; z <= n; z++) {
    vi nw(m + 1, 0);
    vi suf(m + 2, 0);
    for (int i = m; i >= 1; i--) {
      suf[i] = add(suf[i + 1], mult(pow2[i], old[i]));
    }
    for (int i = 1; i <= m; i++) {
      /*
      for(int j=1;j<i;j++)
      {
              nw[j]=add(nw[j],mult(old[i],mult(j,pow2[i-j-1])));
      }
      */
      nw[i] = add(nw[i], mult(old[i], i + 1));
      nw[i] = add(nw[i], mult(mult(i, inverse(pow2[i + 1])), suf[i + 1]));
    }
    old = nw;
  }
  int ans = 0;
  for (int i = 1; i <= m; i++)
    radd(ans, old[i]);
  cout << ans << '\\n';
}