Problem p01809 (C++) — buggy submission, verdict: Time Limit Exceeded

#include "bits/stdc++.h"

#define REP(i, n) for (ll i = 0; i < n; ++i)
#define RREP(i, n) for (ll i = n - 1; i >= 0; --i)
#define FOR(i, m, n) for (ll i = m; i < n; ++i)
#define RFOR(i, m, n) for (ll i = n - 1; i >= m; --i)
#define ALL(v) (v).begin(), (v).end()
#define PB(a) push_back(a)
#define UNIQUE(v) v.erase(unique(ALL(v)), v.end());
#define DUMP(v)                                                                \\
  REP(aa, (v).size()) {                                                        \\
    cout << v[a];                                                              \\
    if (a != v.size() - 1)                                                     \\
      cout << " ";                                                             \\
    else                                                                       \\
      cout << endl;                                                            \\
  }
#define INF 1000000001ll
#define MOD 1000000007ll
#define EPS 1e-9

const int dx[8] = {1, 1, 0, -1, -1, -1, 0, 1};
const int dy[8] = {0, 1, 1, 1, 0, -1, -1, -1};

using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
ll max(ll a, int b) { return max(a, ll(b)); }
ll max(int a, ll b) { return max(ll(a), b); }
ll min(ll a, int b) { return min(a, ll(b)); }
ll min(int a, ll b) { return min(ll(a), b); }
///(?´????????`)(?´????????`)(?´????????`)(?´????????`)(?´????????`)(?´????????`)///
int gcd(int a, int b) {
  if (!b)
    return a;
  return gcd(b, a % b);
}
int fact(int n) {
  int res = 1, i = 2;
  int p = n;
  while (i * i <= p) {
    if (n % i == 0) {
      res *= i;
      while (n % i == 0)
        n /= i;
      if (n != i * i)
        res *= fact(n);
      break;
    }
    ++i;
  }
  if (res == 1)
    return n;
  else
    return res;
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int p, q;
  cin >> p >> q;
  int c = gcd(p, q);
  p /= c;
  q /= c;
  int i = 2;
  cout << fact(q) << endl;
  return 0;
}

Error: TLE

Fixed submission:

#include "bits/stdc++.h"

#define REP(i, n) for (ll i = 0; i < n; ++i)
#define RREP(i, n) for (ll i = n - 1; i >= 0; --i)
#define FOR(i, m, n) for (ll i = m; i < n; ++i)
#define RFOR(i, m, n) for (ll i = n - 1; i >= m; --i)
#define ALL(v) (v).begin(), (v).end()
#define PB(a) push_back(a)
#define UNIQUE(v) v.erase(unique(ALL(v)), v.end());
#define DUMP(v)                                                                \\
  REP(aa, (v).size()) {                                                        \\
    cout << v[a];                                                              \\
    if (a != v.size() - 1)                                                     \\
      cout << " ";                                                             \\
    else                                                                       \\
      cout << endl;                                                            \\
  }
#define INF 1000000001ll
#define MOD 1000000007ll
#define EPS 1e-9

const int dx[8] = {1, 1, 0, -1, -1, -1, 0, 1};
const int dy[8] = {0, 1, 1, 1, 0, -1, -1, -1};

using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
ll max(ll a, int b) { return max(a, ll(b)); }
ll max(int a, ll b) { return max(ll(a), b); }
ll min(ll a, int b) { return min(a, ll(b)); }
ll min(int a, ll b) { return min(ll(a), b); }
///(?´????????`)(?´????????`)(?´????????`)(?´????????`)(?´????????`)(?´????????`)///
int gcd(int a, int b) {
  if (!b)
    return a;
  return gcd(b, a % b);
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int p, q;
  cin >> p >> q;
  int c = gcd(p, q);
  p /= c;
  q /= c;
  int i = 2;
  int res = 1;
  ;
  while (q > 1) {
    if (q % i == 0) {
      res *= i;
      while (q % i == 0)
        q /= i;
    }
    ++i;
  }
  cout << res << endl;
  return 0;
}