Problem p03196 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
#include <unistd.h>

#define fi first
#define se second
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (n); ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define ALL(a) a.begin(), a.end()
#define pb push_back
#define dame                                                                   \
  {                                                                            \
    puts("-1");                                                                \
    return 0;                                                                  \
  }
#define show(x) cerr << #x << " = " << x << endl;

using namespace std;
using ll = long long;
using ld = long double;
using pl = pair<ll, ll>;
ll LINF = 1000000000000000000;

typedef vector<ll> vl;
typedef vector<pl> vp;
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;
}
struct edge {
  ll to, cost;
};

struct dijkstra {
  ll V;
  vector<vector<edge>> G;
  vector<ll> d;

  dijkstra(ll n) { init(n); }

  void init(ll n) {
    V = n;
    G.resize(V);
    d.resize(V);
    rep(i, V) { d[i] = LINF; }
  }

  void add_edge(ll s, ll t, ll cost) {
    edge e;
    e.to = t, e.cost = cost;
    G[s].push_back(e);
  }

  void run(ll s) {
    rep(i, V) { d[i] = LINF; }
    d[s] = 0;
    priority_queue<pl, vector<pl>, greater<pl>> que;
    que.push(pl(0, s));
    while (!que.empty()) {
      pl p = que.top();
      que.pop();
      ll v = p.second;
      if (d[v] < p.first)
        continue;
      for (auto e : G[v]) {
        if (d[e.to] > d[v] + e.cost) {
          d[e.to] = d[v] + e.cost;
          que.push(pl(d[e.to], e.to));
        }
      }
    }
  }
};
// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const ll mod = 1000000007;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
} c(200005);

// Sieve of Eratosthenes
// https://youtu.be/UTVg7wzMWQc?t=2774
struct Sieve {
  int n;
  vector<int> f, primes;
  Sieve(int n = 1) : n(n), f(n + 1) {
    f[0] = f[1] = -1;
    for (ll i = 2; i <= n; ++i) {
      if (f[i])
        continue;
      primes.push_back(i);
      f[i] = i;
      for (ll j = i * i; j <= n; j += i) {
        if (!f[j])
          f[j] = i;
      }
    }
  }
  bool isPrime(int x) { return f[x] == x; }
  vector<int> factorList(int x) {
    vector<int> res;
    while (x != 1) {
      res.push_back(f[x]);
      x /= f[x];
    }
    return res;
  }
  vector<pl> factor(int x) {
    vector<int> fl = factorList(x);
    if (fl.size() == 0)
      return {};
    vector<pl> res(1, pl(fl[0], 0));
    for (int p : fl) {
      if (res.back().first == p) {
        res.back().second++;
      } else {
        res.emplace_back(p, 1);
      }
    }
    return res;
  }
  vector<pair<ll, int>> factor(ll x) {
    vector<pair<ll, int>> res;
    for (int p : primes) {
      int y = 0;
      while (x % p == 0)
        x /= p, ++y;
      if (y != 0)
        res.emplace_back(p, y);
    }
    if (x != 1)
      res.emplace_back(x, 1);
    return res;
  }
};

using data = pair<ll, vector<ll>>;

int main() {
  ll n, p;
  cin >> n >> p;

  if (n == 1) {
    cout << p << endl;
    return 0;
  }

  map<ll, ll> m;
  ll c = p;
  ll ans = 1;

  for (int i = 2; i * i <= p; i++) {
    ll idx = 0;
    while (c % i == 0) {
      c /= i;
      m[i]++;
      idx++;
      if (idx == n) {
        ans *= i;
        idx = 0;
      }
    }
    if (c == 1)
      break;
  }
  // if(c>1) m[c]++;

  cout << ans << endl;
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
#include <unistd.h>

#define fi first
#define se second
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (n); ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define ALL(a) a.begin(), a.end()
#define pb push_back
#define dame                                                                   \
  {                                                                            \
    puts("-1");                                                                \
    return 0;                                                                  \
  }
#define show(x) cerr << #x << " = " << x << endl;

using namespace std;
using ll = long long;
using ld = long double;
using pl = pair<ll, ll>;
ll LINF = 1000000000000000000;

typedef vector<ll> vl;
typedef vector<pl> vp;
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;
}
struct edge {
  ll to, cost;
};

struct dijkstra {
  ll V;
  vector<vector<edge>> G;
  vector<ll> d;

  dijkstra(ll n) { init(n); }

  void init(ll n) {
    V = n;
    G.resize(V);
    d.resize(V);
    rep(i, V) { d[i] = LINF; }
  }

  void add_edge(ll s, ll t, ll cost) {
    edge e;
    e.to = t, e.cost = cost;
    G[s].push_back(e);
  }

  void run(ll s) {
    rep(i, V) { d[i] = LINF; }
    d[s] = 0;
    priority_queue<pl, vector<pl>, greater<pl>> que;
    que.push(pl(0, s));
    while (!que.empty()) {
      pl p = que.top();
      que.pop();
      ll v = p.second;
      if (d[v] < p.first)
        continue;
      for (auto e : G[v]) {
        if (d[e.to] > d[v] + e.cost) {
          d[e.to] = d[v] + e.cost;
          que.push(pl(d[e.to], e.to));
        }
      }
    }
  }
};
// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const ll mod = 1000000007;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
} c(200005);

// Sieve of Eratosthenes
// https://youtu.be/UTVg7wzMWQc?t=2774
struct Sieve {
  int n;
  vector<int> f, primes;
  Sieve(int n = 1) : n(n), f(n + 1) {
    f[0] = f[1] = -1;
    for (ll i = 2; i <= n; ++i) {
      if (f[i])
        continue;
      primes.push_back(i);
      f[i] = i;
      for (ll j = i * i; j <= n; j += i) {
        if (!f[j])
          f[j] = i;
      }
    }
  }
  bool isPrime(int x) { return f[x] == x; }
  vector<int> factorList(int x) {
    vector<int> res;
    while (x != 1) {
      res.push_back(f[x]);
      x /= f[x];
    }
    return res;
  }
  vector<pl> factor(int x) {
    vector<int> fl = factorList(x);
    if (fl.size() == 0)
      return {};
    vector<pl> res(1, pl(fl[0], 0));
    for (int p : fl) {
      if (res.back().first == p) {
        res.back().second++;
      } else {
        res.emplace_back(p, 1);
      }
    }
    return res;
  }
  vector<pair<ll, int>> factor(ll x) {
    vector<pair<ll, int>> res;
    for (int p : primes) {
      int y = 0;
      while (x % p == 0)
        x /= p, ++y;
      if (y != 0)
        res.emplace_back(p, y);
    }
    if (x != 1)
      res.emplace_back(x, 1);
    return res;
  }
};

using data = pair<ll, vector<ll>>;

int main() {
  ll n, p;
  cin >> n >> p;

  if (n == 1) {
    cout << p << endl;
    return 0;
  }

  map<ll, ll> m;
  ll c = p;
  ll ans = 1;

  for (ll i = 2; pow(i, n) <= p; i++) {
    ll pp = pow(i, n);
    while (c % pp == 0) {
      c /= pp;
      ans *= i;
    }
  }
  // if(c>1) m[c]++;

  cout << ans << endl;
  return 0;
}