Problem p04014 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <algorithm>
#include <cassert>
#include <chrono>
#include <cmath>
#include <cstdio>
#include <ctime>
#include <functional>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <vector>
using namespace std;

namespace {
using Integer = long long; //__int128;
template <class T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &val : vec)
    is >> val;
  return is;
}
template <class T> istream &operator,(istream &is, T &val) { return is >> val; }
template <class T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (int i = 0; i < vec.size(); i++)
    os << vec[i] << (i == vec.size() - 1 ? "" : " ");
  return os;
}
template <class T> ostream &operator,(ostream &os, const T &val) {
  return os << " " << val;
}

template <class H> void print(const H &head) { cout << head; }
template <class H, class... T> void print(const H &head, const T &...tail) {
  cout << head << " ";
  print(tail...);
}
template <class... T> void println(const T &...values) {
  print(values...);
  cout << endl;
}

template <class H> void eprint(const H &head) { cerr << head; }
template <class H, class... T> void eprint(const H &head, const T &...tail) {
  cerr << head << " ";
  eprint(tail...);
}
template <class... T> void eprintln(const T &...values) {
  eprint(values...);
  cerr << endl;
}

class range {
  long long start_, end_, step_;

public:
  struct range_iterator {
    long long val, step_;
    range_iterator(long long v, long long step) : val(v), step_(step) {}
    long long operator*() { return val; }
    void operator++() { val += step_; }
    bool operator!=(range_iterator &x) {
      return step_ > 0 ? val < x.val : val > x.val;
    }
  };
  range(long long len) : start_(0), end_(len), step_(1) {}
  range(long long start, long long end) : start_(start), end_(end), step_(1) {}
  range(long long start, long long end, long long step)
      : start_(start), end_(end), step_(step) {}
  range_iterator begin() { return range_iterator(start_, step_); }
  range_iterator end() { return range_iterator(end_, step_); }
};

string operator"" _s(const char *str, size_t size) { return move(string(str)); }
constexpr Integer my_pow(Integer x, Integer k, Integer z = 1) {
  return k == 0    ? z
         : k == 1  ? z * x
         : (k & 1) ? my_pow(x * x, k >> 1, z * x)
                   : my_pow(x * x, k >> 1, z);
}
constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z = 1) {
  return k == 0    ? z % M
         : k == 1  ? z * x % M
         : (k & 1) ? my_pow_mod(x * x % M, k >> 1, M, z * x % M)
                   : my_pow_mod(x * x % M, k >> 1, M, z);
}
constexpr unsigned long long operator"" _ten(unsigned long long value) {
  return my_pow(10, value);
}

inline int k_bit(Integer x, int k) { return (x >> k) & 1; } // 0-indexed

mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(
               chrono::steady_clock::now().time_since_epoch())
               .count());

template <class T> string join(const vector<T> &v, const string &sep) {
  stringstream ss;
  for (int i = 0; i < v.size(); i++) {
    if (i > 0)
      ss << sep;
    ss << v[i];
  }
  return ss.str();
}

string operator*(string s, int k) {
  string ret;
  while (k) {
    if (k & 1)
      ret += s;
    s += s;
    k >>= 1;
  }
  return ret;
}

} // namespace

constexpr long long mod = 9_ten + 7;

long long f(long long x, long long b, long long s = 0) {
  return x < b ? x + s : f(x / b, b, s + x % b);
}

int main() {
  long long n, s;
  cin >> n, s;

  if (s == n) {
    println(n + 1);
    return 0;
  }
  if (s > n) {
    println(-1);
    return 0;
  }

  for (long long i = 2; i * i <= n; i++) {
    if (f(n, i) == s) {
      println(i);
      return 0;
    }
  }

  cerr << "unko" << endl;

  for (long long p = sqrt(n); p > 0; p--) {
    long long q = s - p;
    long long b = (n - q) / p;
    if (f(n, b) == s) {
      println(b);
      return 0;
    }
  }
  println(-1);

  return 0;
}


Fixed submission:
#include <algorithm>
#include <cassert>
#include <chrono>
#include <cmath>
#include <cstdio>
#include <ctime>
#include <functional>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <vector>
using namespace std;

namespace {
using Integer = long long; //__int128;
template <class T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &val : vec)
    is >> val;
  return is;
}
template <class T> istream &operator,(istream &is, T &val) { return is >> val; }
template <class T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (int i = 0; i < vec.size(); i++)
    os << vec[i] << (i == vec.size() - 1 ? "" : " ");
  return os;
}
template <class T> ostream &operator,(ostream &os, const T &val) {
  return os << " " << val;
}

template <class H> void print(const H &head) { cout << head; }
template <class H, class... T> void print(const H &head, const T &...tail) {
  cout << head << " ";
  print(tail...);
}
template <class... T> void println(const T &...values) {
  print(values...);
  cout << endl;
}

template <class H> void eprint(const H &head) { cerr << head; }
template <class H, class... T> void eprint(const H &head, const T &...tail) {
  cerr << head << " ";
  eprint(tail...);
}
template <class... T> void eprintln(const T &...values) {
  eprint(values...);
  cerr << endl;
}

class range {
  long long start_, end_, step_;

public:
  struct range_iterator {
    long long val, step_;
    range_iterator(long long v, long long step) : val(v), step_(step) {}
    long long operator*() { return val; }
    void operator++() { val += step_; }
    bool operator!=(range_iterator &x) {
      return step_ > 0 ? val < x.val : val > x.val;
    }
  };
  range(long long len) : start_(0), end_(len), step_(1) {}
  range(long long start, long long end) : start_(start), end_(end), step_(1) {}
  range(long long start, long long end, long long step)
      : start_(start), end_(end), step_(step) {}
  range_iterator begin() { return range_iterator(start_, step_); }
  range_iterator end() { return range_iterator(end_, step_); }
};

string operator"" _s(const char *str, size_t size) { return move(string(str)); }
constexpr Integer my_pow(Integer x, Integer k, Integer z = 1) {
  return k == 0    ? z
         : k == 1  ? z * x
         : (k & 1) ? my_pow(x * x, k >> 1, z * x)
                   : my_pow(x * x, k >> 1, z);
}
constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z = 1) {
  return k == 0    ? z % M
         : k == 1  ? z * x % M
         : (k & 1) ? my_pow_mod(x * x % M, k >> 1, M, z * x % M)
                   : my_pow_mod(x * x % M, k >> 1, M, z);
}
constexpr unsigned long long operator"" _ten(unsigned long long value) {
  return my_pow(10, value);
}

inline int k_bit(Integer x, int k) { return (x >> k) & 1; } // 0-indexed

mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(
               chrono::steady_clock::now().time_since_epoch())
               .count());

template <class T> string join(const vector<T> &v, const string &sep) {
  stringstream ss;
  for (int i = 0; i < v.size(); i++) {
    if (i > 0)
      ss << sep;
    ss << v[i];
  }
  return ss.str();
}

string operator*(string s, int k) {
  string ret;
  while (k) {
    if (k & 1)
      ret += s;
    s += s;
    k >>= 1;
  }
  return ret;
}

} // namespace

constexpr long long mod = 9_ten + 7;

long long f(long long x, long long b, long long s = 0) {
  return x < b ? x + s : f(x / b, b, s + x % b);
}

int main() {
  long long n, s;
  cin >> n, s;

  if (s == n) {
    println(n + 1);
    return 0;
  }
  if (s > n) {
    println(-1);
    return 0;
  }

  for (long long i = 2; i * i <= n; i++) {
    if (f(n, i) == s) {
      println(i);
      return 0;
    }
  }

  cerr << "unko" << endl;

  for (long long p = sqrt(n); p > 0; p--) {
    long long q = s - p;
    long long b = (n - q) / p;
    // if( f(n,b) == s){
    if (b * p + q == n && b > p && b > q && n / b == p && n % b == q) {
      println(b);
      return 0;
    }
  }
  println(-1);

  return 0;
}