Problem p03194 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> l_l;
typedef pair<int, int> i_i;
typedef vector<ll> vel;
typedef vector<int> vei;
typedef vector<char> vec;
typedef vector<bool> veb;
typedef vector<string> ves;
typedef vector<vector<ll>> ve_vel;
typedef vector<vector<int>> ve_vei;
typedef vector<vector<char>> ve_vec;
typedef vector<vector<bool>> ve_veb;
typedef vector<vector<string>> ve_ves;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i < (int)(n); i++)
#define rep2(i, n) for (int i = 2; i < (int)(n); i++)
#define repk(i, k, n) for (int i = k; i < (int)(n); i++)
#define fs first
#define sc second
#define pub push_back
#define pob pop_back
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define maxel(a) *max_element(all(a))
#define minel(a) *min_element(all(a))
#define acc accumulate
#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
#define mod (1000000007)
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

ll beki(ll a, ll n) {
  if (n == 0) {
    return 1;
  }
  ll ans = beki(a, n / 2);
  ans = ans * ans;
  if (n % 2 == 1)
    ans = ans * a;
  return ans;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  ll N, P;
  cin >> N >> P;

  if (N == 1) {
    cout << P << endl;
    return 0;
  }
  if (P == 1) {
    cout << 1 << endl;
    return 0;
  }

  ll ans = 1;
  for (ll i = 1; beki(i, N) <= P; i++) {
    ll c = beki(i, N);
    if (P % c == 0)
      ans = i;
  }
  cout << ans << endl;
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> l_l;
typedef pair<int, int> i_i;
typedef vector<ll> vel;
typedef vector<int> vei;
typedef vector<char> vec;
typedef vector<bool> veb;
typedef vector<string> ves;
typedef vector<vector<ll>> ve_vel;
typedef vector<vector<int>> ve_vei;
typedef vector<vector<char>> ve_vec;
typedef vector<vector<bool>> ve_veb;
typedef vector<vector<string>> ve_ves;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i < (int)(n); i++)
#define rep2(i, n) for (int i = 2; i < (int)(n); i++)
#define repk(i, k, n) for (int i = k; i < (int)(n); i++)
#define fs first
#define sc second
#define pub push_back
#define pob pop_back
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define maxel(a) *max_element(all(a))
#define minel(a) *min_element(all(a))
#define acc accumulate
#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
#define mod (1000000007)
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

ll beki(ll a, ll n) {
  if (n == 0) {
    return 1;
  }
  ll ans = beki(a, n / 2);
  ans = ans * ans;
  if (n % 2 == 1)
    ans = ans * a;
  return ans;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  ll N, P;
  cin >> N >> P;

  if (N == 1) {
    cout << P << endl;
    return 0;
  }
  if (N >= 41) {
    cout << 1 << endl;
    return 0;
  }
  if (P == 1) {
    cout << 1 << endl;
    return 0;
  }

  ll ans = 1;
  for (ll i = 1; beki(i, N) <= P; i++) {
    ll c = beki(i, N);
    if (P % c == 0)
      ans = i;
  }
  cout << ans << endl;
  return 0;
}