Problem p03196 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#define ll long long
#define ull unsigned long long
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(a, b) for (int a = 0; a < (b); ++a)
#define REP1(i, n) for (int i = 1; i <= (n); ++i)
#define debug(x) cerr << #x << ": " << x << '\n'
#define all(x) (x).begin(), (x).end()
#define YES() printf("YES\n")
#define NO() printf("NO\n")
#define isYES(x) printf("%s\n", (x) ? "YES" : "NO")
#define Yes() printf("Yes\n")
#define No() printf("No\n")
#define isYes(x) printf("%s\n", (x) ? "Yes" : "No")
#define isPossible(x) printf("%s\n", (x) ? "Possible" : "Impossible")
#define SZ(x) ((int)(x).size())
#define pb push_back
#define mp make_pair
#define INF (1 << 29)

// const long long INF = 1LL<<60;

#define Sp(p) cout << setprecision(25) << fixed << p << endl
#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
#define X first
#define Y second
#define pie 3.14159265358979323846
using namespace std;
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
typedef pair<int, P> PP;
typedef pair<ll, LP> LPP;
template <class T = int> T in() {
  T x;
  cin >> x;
  return (x);
}
template <class T> void print(T &x) { cout << x << '\n'; }

const int MOD = (int)1e9 + 7;
const int mod = (int)998244353;

const int MAX = 510000;
ll fac[MAX], finv[MAX], inv[MAX];
void COMint() {
  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;
  }
}
ll COM(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;
}
ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  if (a > b) {
    swap(a, b);
  }
  return gcd(a, b % a);
}
ll lcm(ll a, ll b) {
  ll g;
  g = gcd(a, b);
  return b / g * a;
}
bool compare_by_b(pair<int, int> a, pair<int, int> b) {
  if (a.second != b.second) {
    return a.second < b.second;
  } else {
    return a.first < b.first;
  }
}

bool compare_by_a(pair<int, int> a, pair<int, int> b) {
  if (a.first != b.first) {
    return a.first < b.first;
  } else {
    return a.second < b.second;
  }
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

ll RS(ll N, ll P) {
  if (P == 0) {
    return 1;
  } else {
    if (P % 2 == 0) {
      ll t = RS(N, P / 2);
      return t * t;
    } else {
      return N * RS(N, P - 1);
    }
  }
}
bool greater_pair(pair<ll, ll> a, pair<ll, ll> b) {
  if (a.first != b.first) {
    return a.first > b.first;
  } else {
    return a.second > b.second;
  }
}
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  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 {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= 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 {
    mint res(*this);
    return res /= a;
  }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
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(2000005);

string func(string S) {
  if (S.length() < 1) {
    return "";
  } else {
    return S.substr(1);
  }
}

int main() {
  ios::sync_with_stdio(false);
  ll N, P;
  cin >> N >> P;
  ll ans = 1;
  if (N == 1) {
    cout << P << endl;
  } else if (N > 40) {
    cout << 1 << endl;
  } else {
    for (int i = 2; i <= sqrt(P); ++i) {
      ll p = RS(i, N);
      // ll p=pow(i,N);
      while (P % p == 0) {
        P /= p;
        ans *= i;
      }
    }
    cout << ans << endl;
  }
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
#define ll long long
#define ull unsigned long long
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(a, b) for (int a = 0; a < (b); ++a)
#define REP1(i, n) for (int i = 1; i <= (n); ++i)
#define debug(x) cerr << #x << ": " << x << '\n'
#define all(x) (x).begin(), (x).end()
#define YES() printf("YES\n")
#define NO() printf("NO\n")
#define isYES(x) printf("%s\n", (x) ? "YES" : "NO")
#define Yes() printf("Yes\n")
#define No() printf("No\n")
#define isYes(x) printf("%s\n", (x) ? "Yes" : "No")
#define isPossible(x) printf("%s\n", (x) ? "Possible" : "Impossible")
#define SZ(x) ((int)(x).size())
#define pb push_back
#define mp make_pair
#define INF (1 << 29)

// const long long INF = 1LL<<60;

#define Sp(p) cout << setprecision(25) << fixed << p << endl
#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
#define X first
#define Y second
#define pie 3.14159265358979323846
using namespace std;
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
typedef pair<int, P> PP;
typedef pair<ll, LP> LPP;
template <class T = int> T in() {
  T x;
  cin >> x;
  return (x);
}
template <class T> void print(T &x) { cout << x << '\n'; }

const int MOD = (int)1e9 + 7;
const int mod = (int)998244353;

const int MAX = 510000;
ll fac[MAX], finv[MAX], inv[MAX];
void COMint() {
  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;
  }
}
ll COM(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;
}
ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  if (a > b) {
    swap(a, b);
  }
  return gcd(a, b % a);
}
ll lcm(ll a, ll b) {
  ll g;
  g = gcd(a, b);
  return b / g * a;
}
bool compare_by_b(pair<int, int> a, pair<int, int> b) {
  if (a.second != b.second) {
    return a.second < b.second;
  } else {
    return a.first < b.first;
  }
}

bool compare_by_a(pair<int, int> a, pair<int, int> b) {
  if (a.first != b.first) {
    return a.first < b.first;
  } else {
    return a.second < b.second;
  }
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

ll RS(ll N, ll P) {
  if (P == 0) {
    return 1;
  } else {
    if (P % 2 == 0) {
      ll t = RS(N, P / 2);
      return t * t;
    } else {
      return N * RS(N, P - 1);
    }
  }
}
bool greater_pair(pair<ll, ll> a, pair<ll, ll> b) {
  if (a.first != b.first) {
    return a.first > b.first;
  } else {
    return a.second > b.second;
  }
}
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  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 {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= 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 {
    mint res(*this);
    return res /= a;
  }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
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(2000005);

string func(string S) {
  if (S.length() < 1) {
    return "";
  } else {
    return S.substr(1);
  }
}

int main() {
  ios::sync_with_stdio(false);
  ll N, P;
  cin >> N >> P;
  ll ans = 1;
  if (N == 1) {
    cout << P << endl;
  } else if (N > 40) {
    cout << 1 << endl;
  } else {
    for (int i = 2; i <= sqrt(P); ++i) {
      ll p = RS(i, N);
      if (p > P)
        break;
      // ll p=pow(i,N);
      while (P % p == 0) {
        P /= p;
        ans *= i;
      }
    }
    cout << ans << endl;
  }
  return 0;
}