Problem p03196 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <stack>
#include <string>
#include <time.h>
#include <vector>
#define rep(i, n) for (int i = 0; i < n; i++)
#define int long long
#define ggr                                                                    \
  getchar();                                                                   \
  getchar();                                                                   \
  return 0;
#define prique priority_queue
constexpr auto mod = 1000000007;
#define inf 1e15
#define key 1e9
using namespace std;
typedef pair<int, int> P;
void yes() { cout << "Yay!" << endl; }
void no() { cout << ":(" << endl; }
template <class T> inline void chmax(T &a, T b) { a = std::max(a, b); }
template <class T> inline void chmin(T &a, T b) { a = std::min(a, b); }

// combination(Nが小さい時はこれを使う)
const int MAX = 300000;
int fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % mod;
    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
    finv[i] = finv[i - 1] * inv[i] % mod;
  }
}
int COMB(int n, int k) {
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
}

bool prime(int n) {
  int cnt = 0;
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0)
      cnt++;
  }
  if (cnt != 1)
    return false;
  else
    return n != 1;
}
int gcd(int x, int y) {
  if (y == 0)
    return x;
  return gcd(y, x % y);
}
int lcm(int x, int y) { return x / gcd(x, y) * y; }

// 繰り返し二乗法（Nが大きい時の場合のcombination)
int mod_pow(int x, int y, int m) {
  int res = 1;
  while (y) {
    if (y & 1) {
      res = res * x % m;
    }
    x = x * x % m;
    y >>= 1;
  }
  return res;
}
int kai(int x, int y) {
  int res = 1;
  for (int i = x - y + 1; i <= x; i++) {
    res *= (i % mod);
    res %= mod;
  }
  return res;
}
int comb(int x, int y) {
  if (y > x)
    return 0;
  return kai(x, y) * mod_pow(kai(y, y), mod - 2, mod) % mod;
}
// UnionFind
class UnionFind {
protected:
  int *par, *rank, *size;

public:
  UnionFind(unsigned int size) {
    par = new int[size];
    rank = new int[size];
    this->size = new int[size];
    rep(i, size) {
      par[i] = i;
      rank[i] = 0;
      this->size[i] = 1;
    }
  }
  int find(int n) {
    if (par[n] == n)
      return n;
    return par[n] = find(par[n]);
  }
  void unite(int n, int m) {
    n = find(n);
    m = find(m);
    if (n == m)
      return;
    if (rank[n] < rank[m]) {
      par[n] = m;
      size[m] += size[n];
    } else {
      par[m] = n;
      size[n] += size[m];
      if (rank[n] == rank[m])
        rank[n]++;
    }
  }
  bool same(int n, int m) { return find(n) == find(m); }
  int getsize(int n) { return size[find(n)]; }
};
map<int, int> mp;
signed main() {
  int n, p;
  cin >> n >> p;
  int memo = p, ans = 1;
  for (int i = 2; i <= sqrt(p); i++) {
    if (prime(i)) {
      while (memo % i == 0) {
        memo /= i;
        mp[i]++;
      }
    }
  }
  if (memo != 1)
    mp[memo]++;
  for (auto x : mp)
    ans *= pow(x.first, x.second / n);
  cout << ans << endl;
  ggr
}


Fixed submission:
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <stack>
#include <string>
#include <time.h>
#include <vector>
#define rep(i, n) for (int i = 0; i < n; i++)
#define int long long
#define ggr                                                                    \
  getchar();                                                                   \
  getchar();                                                                   \
  return 0;
#define prique priority_queue
constexpr auto mod = 1000000007;
#define inf 1e15
#define key 1e9
using namespace std;
typedef pair<int, int> P;
void yes() { cout << "Yay!" << endl; }
void no() { cout << ":(" << endl; }
template <class T> inline void chmax(T &a, T b) { a = std::max(a, b); }
template <class T> inline void chmin(T &a, T b) { a = std::min(a, b); }

// combination(Nが小さい時はこれを使う)
const int MAX = 300000;
int fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % mod;
    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
    finv[i] = finv[i - 1] * inv[i] % mod;
  }
}
int COMB(int n, int k) {
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
}

bool prime(int n) {
  int cnt = 0;
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0)
      cnt++;
  }
  if (cnt != 1)
    return false;
  else
    return n != 1;
}
int gcd(int x, int y) {
  if (y == 0)
    return x;
  return gcd(y, x % y);
}
int lcm(int x, int y) { return x / gcd(x, y) * y; }

// 繰り返し二乗法（Nが大きい時の場合のcombination)
int mod_pow(int x, int y, int m) {
  int res = 1;
  while (y) {
    if (y & 1) {
      res = res * x % m;
    }
    x = x * x % m;
    y >>= 1;
  }
  return res;
}
int kai(int x, int y) {
  int res = 1;
  for (int i = x - y + 1; i <= x; i++) {
    res *= (i % mod);
    res %= mod;
  }
  return res;
}
int comb(int x, int y) {
  if (y > x)
    return 0;
  return kai(x, y) * mod_pow(kai(y, y), mod - 2, mod) % mod;
}
// UnionFind
class UnionFind {
protected:
  int *par, *rank, *size;

public:
  UnionFind(unsigned int size) {
    par = new int[size];
    rank = new int[size];
    this->size = new int[size];
    rep(i, size) {
      par[i] = i;
      rank[i] = 0;
      this->size[i] = 1;
    }
  }
  int find(int n) {
    if (par[n] == n)
      return n;
    return par[n] = find(par[n]);
  }
  void unite(int n, int m) {
    n = find(n);
    m = find(m);
    if (n == m)
      return;
    if (rank[n] < rank[m]) {
      par[n] = m;
      size[m] += size[n];
    } else {
      par[m] = n;
      size[n] += size[m];
      if (rank[n] == rank[m])
        rank[n]++;
    }
  }
  bool same(int n, int m) { return find(n) == find(m); }
  int getsize(int n) { return size[find(n)]; }
};
map<int, int> mp;
signed main() {
  int n, p;
  cin >> n >> p;
  int memo = p, ans = 1;
  for (int i = 2; i <= sqrt(p); i++) {
    while (memo % i == 0) {
      memo /= i;
      mp[i]++;
    }
  }
  if (memo != 1)
    mp[memo]++;
  for (auto x : mp)
    ans *= pow(x.first, x.second / n);
  cout << ans << endl;
  ggr
}