Problem p02541 (C++) — buggy submission, verdict: Runtime Error

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author Gosu_Hiroo
 */

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using VI = vector<int>;
using VL = vector<long long>;
using PII = pair<int, int>;
using PLL = pair<long long, long long>;

// #pragma GCC optimize("O3")
// #pragma GCC target("avx2")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// #pragma GCC optimize("Ofast")

#define G(size_1) vector<vector<int>>(size_1, vector<int>())
#define SZ(x) ((long long)(x).size())
#define READ                                                                   \\
  ({                                                                           \\
    long long t;                                                               \\
    cin >> t;                                                                  \\
    t;                                                                         \\
  })

#define FOR(i, _begin, _end)                                                   \\
  for (__typeof(_end) end = _end, begin = _begin,                              \\
                      i = (begin) - ((begin) > (end));                         \\
       i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))
#define REP(i, end) for (__typeof(end) i = 0, _len = (end); i < (_len); i += 1)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define F first
#define S second
#define y0 y3487465
#define y1 y8687969
#define j0 j1347829
#define j1 j234892
#define BIT(n) (1LL << (n))
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());
#define EB emplace_back
#define PB push_back
#define fcout cout << fixed << setprecision(12)
#define fcerr cerr << fixed << setprecision(12)
#define print(x) cout << (x) << '\\n'
#define printE(x) cout << (x) << '\\n';
#define fprint(x) cout << fixed << setprecision(12) << (x) << '\\n';
#define BYE(a)                                                                 \\
  do {                                                                         \\
    cout << (a) << endl;                                                       \\
    return;                                                                    \\
  } while (false)

#ifdef DEBUG
#define DBG(args...)                                                           \\
  {                                                                            \\
    string _s = #args;                                                         \\
    replace(_s.begin(), _s.end(), ',', ' ');                                   \\
    stringstream _ss(_s);                                                      \\
    istream_iterator<string> _it(_ss);                                         \\
    _err(cerr, _it, args);                                                     \\
  }
#define ERR(args...)                                                           \\
  {                                                                            \\
    string _s = #args;                                                         \\
    replace(_s.begin(), _s.end(), ',', ' ');                                   \\
    stringstream _ss(_s);                                                      \\
    istream_iterator<string> _it(_ss);                                         \\
    _err(std::cerr, _it, args);                                                \\
  }
#else
#define DBG(args...) {};
#define ERR(args...) {};
#endif
void _err(std::ostream &cerr, istream_iterator<string> it) { cerr << endl; }
template <typename T, typename... Args>
void _err(std::ostream &cerr, istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "  ";
  _err(cerr, ++it, args...);
}

const double PI = 2 * acos(.0);
const int INF = 0x3f3f3f3f;

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 (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> T ceil(T a, T b) { return (a + b - 1) / b; }

template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &V) {
  is >> V.F >> V.S;
  return is;
}

template <typename T> istream &operator>>(istream &is, vector<T> &V) {
  for (auto &&ele : V)
    is >> ele;
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> V) {
  os << "[";
  int cnt = 0;
  T curr;
  if (!V.empty()) {
    for (int i = 0; i < V.size() - 1; ++i) {
      if (V[i] == curr)
        cnt++;
      else
        cnt = 0;
      if (cnt == 4)
        os << "... ";
      if (cnt < 4)
        os << i << ":" << V[i] << " ";
      curr = V[i];
    }
    os << V.size() - 1 << ":" << V.back();
  }
  os << "]\\n";
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> P) {
  os << "(";
  os << P.first << "," << P.second;
  os << ")";
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const set<T, U> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}\\n";
  return os;
}

template <typename K, typename H, typename P>
ostream &operator<<(ostream &os, const unordered_set<K, H, P> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}\\n";
  return os;
}

template <typename K, typename C>
ostream &operator<<(ostream &os, const multiset<K, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}";
  return os;
}

template <typename K, typename T, typename C>
ostream &operator<<(ostream &os, const map<K, T, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << "(";
      os << it->first << "," << it->second;
      os << ") ";
      it++;
    }
    os << "(";
    os << it->first << "," << it->second;
    os << ")";
  }
  os << "}\\n";
  return os;
}

template <typename K, typename T, typename C>
ostream &operator<<(ostream &os, const unordered_map<K, T, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << "(";
      os << it->first << "," << it->second;
      os << ") ";
      it++;
    }
    os << "(";
    os << it->first << "," << it->second;
    os << ")";
  }
  os << "}\\n";
  return os;
}

template <typename T> ostream &operator<<(ostream &os, const deque<T> V) {
  os << "[";
  if (!V.empty()) {
    for (int i = 0; i < V.size() - 1; ++i) {
      os << V[i] << "->";
    }
    if (!V.empty())
      os << V.back();
  }
  os << "]\\n";
  return os;
};

template <typename T, typename Cont, typename Comp>
ostream &operator<<(ostream &os, const priority_queue<T, Cont, Comp> V) {
  priority_queue<T, Cont, Comp> _V = V;
  os << "[";
  if (!_V.empty()) {
    while (_V.size() > 1) {
      os << _V.top() << "->";
      _V.pop();
    }
    os << _V.top();
  }
  os << "]\\n";
  return os;
};

template <class F> struct y_combinator {
  F f; // the lambda will be stored here

  // a forwarding operator():
  template <class... Args> decltype(auto) operator()(Args &&...args) const {
    // we pass ourselves to f, then the arguments.
    // the lambda should take the first argument as `auto&& recurse` or similar.
    return f(*this, std::forward<Args>(args)...);
  }
};
// helper function that deduces the type of the lambda:
template <class F> y_combinator<std::decay_t<F>> recursive(F &&f) {
  return {std::forward<F>(f)};
}

struct hash_pair {
  template <class T1, class T2> size_t operator()(const pair<T1, T2> &p) const {
    auto hash1 = hash<T1>{}(p.first);
    auto hash2 = hash<T2>{}(p.second);
    return hash1 ^ hash2;
  }
};

template <typename T, typename U> std::vector<T> multi_vector(int n, U v) {
  return std::vector<T>(n, v);
}

template <typename U, typename... Args> auto multi_vector(int n, Args... args) {
  auto val = multi_vector<U>(std::forward<Args>(args)...);
  return std::vector<decltype(val)>(n, std::move(val));
}

map<ll, ll> factorize(ll N) {
  map<ll, ll> factors;
  while (!(N & 1))
    N >>= 1, factors[2]++;
  while (N % 3 == 0)
    N /= 3, factors[3]++;
  for (ll i = 5; i * i <= N; i += 6) {
    while (N % i == 0)
      N /= i, factors[i]++;
    while (N % (i + 2) == 0)
      N /= i + 2, factors[i + 2]++;
  }
  if (N > 1)
    factors[N]++;
  return factors;
}

ll power(ll x, ll y) {
  assert(y >= 0);
  ll res = 1;
  while (y) {
    if (y & 1)
      res *= x;
    y = y >> 1;
    x *= x;
  }
  return res;
}

#ifndef ATCODER_MATH_HPP
#define ATCODER_MATH_HPP 1

#include <algorithm>
#include <cassert>
#include <tuple>
#include <vector>
#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1

#include <utility>

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
  x %= m;
  if (x < 0)
    x += m;
  return x;
}

// Fast moduler by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
  unsigned int _m;
  unsigned long long im;

  // @param m `1 <= m`
  barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

  // @return m
  unsigned int umod() const { return _m; }

  // @param a `0 <= a < m`
  // @param b `0 <= b < m`
  // @return `a * b % m`
  unsigned int mul(unsigned int a, unsigned int b) const {
    // [1] m = 1
    // a = b = im = 0, so okay

    // [2] m >= 2
    // im = ceil(2^64 / m)
    // -> im * m = 2^64 + r (0 <= r < m)
    // let z = a*b = c*m + d (0 <= c, d < m)
    // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
    // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) <
    // 2^64 * 2
    // ((ab * im) >> 64) == c or c + 1
    unsigned long long z = a;
    z *= b;
#ifdef _MSC_VER
    unsigned long long x;
    _umul128(z, im, &x);
#else
    unsigned long long x =
        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
    unsigned int v = (unsigned int)(z - x * _m);
    if (_m <= v)
      v += _m;
    return v;
  }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
  if (m == 1)
    return 0;
  unsigned int _m = (unsigned int)(m);
  unsigned long long r = 1;
  unsigned long long y = safe_mod(x, m);
  while (n) {
    if (n & 1)
      r = (r * y) % _m;
    y = (y * y) % _m;
    n >>= 1;
  }
  return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
  if (n <= 1)
    return false;
  if (n == 2 || n == 7 || n == 61)
    return true;
  if (n % 2 == 0)
    return false;
  long long d = n - 1;
  while (d % 2 == 0)
    d /= 2;
  for (long long a : {2, 7, 61}) {
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
  a = safe_mod(a, b);
  if (a == 0)
    return {b, 0};

  // Contracts:
  // [1] s - m0 * a = 0 (mod b)
  // [2] t - m1 * a = 0 (mod b)
  // [3] s * |m1| + t * |m0| <= b
  long long s = b, t = a;
  long long m0 = 0, m1 = 1;

  while (t) {
    long long u = s / t;
    s -= t * u;
    m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b

    // [3]:
    // (s - t * u) * |m1| + t * |m0 - m1 * u|
    // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
    // = s * |m1| + t * |m0| <= b

    auto tmp = s;
    s = t;
    t = tmp;
    tmp = m0;
    m0 = m1;
    m1 = tmp;
  }
  // by [3]: |m0| <= b/g
  // by g != b: |m0| < b/g
  if (m0 < 0)
    m0 += b / s;
  return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
  if (m == 2)
    return 1;
  if (m == 167772161)
    return 3;
  if (m == 469762049)
    return 3;
  if (m == 754974721)
    return 11;
  if (m == 998244353)
    return 3;
  int divs[20] = {};
  divs[0] = 2;
  int cnt = 1;
  int x = (m - 1) / 2;
  while (x % 2 == 0)
    x /= 2;
  for (int i = 3; (long long)(i)*i <= x; i += 2) {
    if (x % i == 0) {
      divs[cnt++] = i;
      while (x % i == 0) {
        x /= i;
      }
    }
  }
  if (x > 1) {
    divs[cnt++] = x;
  }
  for (int g = 2;; g++) {
    bool ok = true;
    for (int i = 0; i < cnt; i++) {
      if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
        ok = false;
        break;
      }
    }
    if (ok)
      return g;
  }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

} // namespace internal

} // namespace atcoder

#endif // ATCODER_INTERNAL_MATH_HPP

namespace atcoder {

long long pow_mod(long long x, long long n, int m) {
  assert(0 <= n && 1 <= m);
  if (m == 1)
    return 0;
  internal::barrett bt((unsigned int)(m));
  unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
  while (n) {
    if (n & 1)
      r = bt.mul(r, y);
    y = bt.mul(y, y);
    n >>= 1;
  }
  return r;
}

long long inv_mod(long long x, long long m) {
  assert(1 <= m);
  auto z = internal::inv_gcd(x, m);
  assert(z.first == 1);
  return z.second;
}

// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long> &r,
                                    const std::vector<long long> &m) {
  assert(r.size() == m.size());
  int n = int(r.size());
  // Contracts: 0 <= r0 < m0
  long long r0 = 0, m0 = 1;
  for (int i = 0; i < n; i++) {
    assert(1 <= m[i]);
    long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
    if (m0 < m1) {
      std::swap(r0, r1);
      std::swap(m0, m1);
    }
    if (m0 % m1 == 0) {
      if (r0 % m1 != r1)
        return {0, 0};
      continue;
    }
    // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)

    // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
    // r2 % m0 = r0
    // r2 % m1 = r1
    // -> (r0 + x*m0) % m1 = r1
    // -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1)
    // -> x = (r1 - r0) / g * inv(u0) (mod u1)

    // im = inv(u0) (mod u1) (0 <= im < u1)
    long long g, im;
    std::tie(g, im) = internal::inv_gcd(m0, m1);

    long long u1 = (m1 / g);
    // |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
    if ((r1 - r0) % g)
      return {0, 0};

    // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
    long long x = (r1 - r0) / g % u1 * im % u1;

    // |r0| + |m0 * x|
    // < m0 + m0 * (u1 - 1)
    // = m0 + m0 * m1 / g - m0
    // = lcm(m0, m1)
    r0 += x * m0;
    m0 *= u1; // -> lcm(m0, m1)
    if (r0 < 0)
      r0 += m0;
  }
  return {r0, m0};
}

long long floor_sum(long long n, long long m, long long a, long long b) {
  long long ans = 0;
  if (a >= m) {
    ans += (n - 1) * n * (a / m) / 2;
    a %= m;
  }
  if (b >= m) {
    ans += n * (b / m);
    b %= m;
  }

  long long y_max = (a * n + b) / m, x_max = (y_max * m - b);
  if (y_max == 0)
    return ans;
  ans += (n - (x_max + a - 1) / a) * y_max;
  ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
  return ans;
}

} // namespace atcoder

#endif // ATCODER_MATH_HPP

using namespace atcoder;
class BSumIsMultiple {
public:
  void solve(std::istream &cin, std::ostream &cout, std::ostream &cerr) {
    ll N;
    cin >> N;
    N *= 2;
    auto factors = factorize(N);
    ll n = SZ(factors);
    VL b(n);
    {
      int i = 0;
      for (auto [x, a] : factors) {
        b[i++] = power(x, a);
      }
    }
    ll ans = N - 1;
    if (N == 1)
      BYE(1);
    if (n == 1) {
      BYE(b[0] - 1);
    }
    REP(mask, BIT(n)) {
      ll p = 1, q = 1;
      REP(i, n) if (mask & BIT(i)) p *= b[i];
      else q *= b[i];
      ll b = inv_mod(q, p);
      DBG(p, q, b)
      if (p == 1 || q == 1)
        continue;
      if (b * q > 1 && (b * q - 1) / p > 0)
        chmin(ans, b * q - 1);
    }
    print(ans);
  }
};

#undef int
int main() {

  BSumIsMultiple solver;
  std::istream &in(std::cin);
  std::ostream &out(std::cout);
  std::ostringstream err;
  in.tie(0);
  ios::sync_with_stdio(0);
  solver.solve(in, out, err);
  return 0;
}


Error: 0

Fixed submission:

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author Gosu_Hiroo
 */

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using VI = vector<int>;
using VL = vector<long long>;
using PII = pair<int, int>;
using PLL = pair<long long, long long>;

// #pragma GCC optimize("O3")
// #pragma GCC target("avx2")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// #pragma GCC optimize("Ofast")

#define G(size_1) vector<vector<int>>(size_1, vector<int>())
#define SZ(x) ((long long)(x).size())
#define READ                                                                   \\
  ({                                                                           \\
    long long t;                                                               \\
    cin >> t;                                                                  \\
    t;                                                                         \\
  })

#define FOR(i, _begin, _end)                                                   \\
  for (__typeof(_end) end = _end, begin = _begin,                              \\
                      i = (begin) - ((begin) > (end));                         \\
       i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))
#define REP(i, end) for (__typeof(end) i = 0, _len = (end); i < (_len); i += 1)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define F first
#define S second
#define y0 y3487465
#define y1 y8687969
#define j0 j1347829
#define j1 j234892
#define BIT(n) (1LL << (n))
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());
#define EB emplace_back
#define PB push_back
#define fcout cout << fixed << setprecision(12)
#define fcerr cerr << fixed << setprecision(12)
#define print(x) cout << (x) << '\\n'
#define printE(x) cout << (x) << '\\n';
#define fprint(x) cout << fixed << setprecision(12) << (x) << '\\n';
#define BYE(a)                                                                 \\
  do {                                                                         \\
    cout << (a) << endl;                                                       \\
    return;                                                                    \\
  } while (false)

#ifdef DEBUG
#define DBG(args...)                                                           \\
  {                                                                            \\
    string _s = #args;                                                         \\
    replace(_s.begin(), _s.end(), ',', ' ');                                   \\
    stringstream _ss(_s);                                                      \\
    istream_iterator<string> _it(_ss);                                         \\
    _err(cerr, _it, args);                                                     \\
  }
#define ERR(args...)                                                           \\
  {                                                                            \\
    string _s = #args;                                                         \\
    replace(_s.begin(), _s.end(), ',', ' ');                                   \\
    stringstream _ss(_s);                                                      \\
    istream_iterator<string> _it(_ss);                                         \\
    _err(std::cerr, _it, args);                                                \\
  }
#else
#define DBG(args...) {};
#define ERR(args...) {};
#endif
void _err(std::ostream &cerr, istream_iterator<string> it) { cerr << endl; }
template <typename T, typename... Args>
void _err(std::ostream &cerr, istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "  ";
  _err(cerr, ++it, args...);
}

const double PI = 2 * acos(.0);
const int INF = 0x3f3f3f3f;

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 (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> T ceil(T a, T b) { return (a + b - 1) / b; }

template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &V) {
  is >> V.F >> V.S;
  return is;
}

template <typename T> istream &operator>>(istream &is, vector<T> &V) {
  for (auto &&ele : V)
    is >> ele;
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> V) {
  os << "[";
  int cnt = 0;
  T curr;
  if (!V.empty()) {
    for (int i = 0; i < V.size() - 1; ++i) {
      if (V[i] == curr)
        cnt++;
      else
        cnt = 0;
      if (cnt == 4)
        os << "... ";
      if (cnt < 4)
        os << i << ":" << V[i] << " ";
      curr = V[i];
    }
    os << V.size() - 1 << ":" << V.back();
  }
  os << "]\\n";
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> P) {
  os << "(";
  os << P.first << "," << P.second;
  os << ")";
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const set<T, U> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}\\n";
  return os;
}

template <typename K, typename H, typename P>
ostream &operator<<(ostream &os, const unordered_set<K, H, P> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}\\n";
  return os;
}

template <typename K, typename C>
ostream &operator<<(ostream &os, const multiset<K, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}";
  return os;
}

template <typename K, typename T, typename C>
ostream &operator<<(ostream &os, const map<K, T, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << "(";
      os << it->first << "," << it->second;
      os << ") ";
      it++;
    }
    os << "(";
    os << it->first << "," << it->second;
    os << ")";
  }
  os << "}\\n";
  return os;
}

template <typename K, typename T, typename C>
ostream &operator<<(ostream &os, const unordered_map<K, T, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << "(";
      os << it->first << "," << it->second;
      os << ") ";
      it++;
    }
    os << "(";
    os << it->first << "," << it->second;
    os << ")";
  }
  os << "}\\n";
  return os;
}

template <typename T> ostream &operator<<(ostream &os, const deque<T> V) {
  os << "[";
  if (!V.empty()) {
    for (int i = 0; i < V.size() - 1; ++i) {
      os << V[i] << "->";
    }
    if (!V.empty())
      os << V.back();
  }
  os << "]\\n";
  return os;
};

template <typename T, typename Cont, typename Comp>
ostream &operator<<(ostream &os, const priority_queue<T, Cont, Comp> V) {
  priority_queue<T, Cont, Comp> _V = V;
  os << "[";
  if (!_V.empty()) {
    while (_V.size() > 1) {
      os << _V.top() << "->";
      _V.pop();
    }
    os << _V.top();
  }
  os << "]\\n";
  return os;
};

template <class F> struct y_combinator {
  F f; // the lambda will be stored here

  // a forwarding operator():
  template <class... Args> decltype(auto) operator()(Args &&...args) const {
    // we pass ourselves to f, then the arguments.
    // the lambda should take the first argument as `auto&& recurse` or similar.
    return f(*this, std::forward<Args>(args)...);
  }
};
// helper function that deduces the type of the lambda:
template <class F> y_combinator<std::decay_t<F>> recursive(F &&f) {
  return {std::forward<F>(f)};
}

struct hash_pair {
  template <class T1, class T2> size_t operator()(const pair<T1, T2> &p) const {
    auto hash1 = hash<T1>{}(p.first);
    auto hash2 = hash<T2>{}(p.second);
    return hash1 ^ hash2;
  }
};

template <typename T, typename U> std::vector<T> multi_vector(int n, U v) {
  return std::vector<T>(n, v);
}

template <typename U, typename... Args> auto multi_vector(int n, Args... args) {
  auto val = multi_vector<U>(std::forward<Args>(args)...);
  return std::vector<decltype(val)>(n, std::move(val));
}

map<ll, int> factorize(ll N) {
  map<ll, int> factors;
  while (!(N & 1))
    N >>= 1, factors[2]++;
  while (N % 3 == 0)
    N /= 3, factors[3]++;
  for (ll i = 5; i * i <= N; i += 6) {
    while (N % i == 0)
      N /= i, factors[i]++;
    while (N % (i + 2) == 0)
      N /= i + 2, factors[i + 2]++;
  }
  if (N > 1)
    factors[N]++;
  return factors;
}

ll power(ll x, ll y) {
  assert(y >= 0);
  ll res = 1;
  while (y) {
    if (y & 1)
      res *= x;
    y = y >> 1;
    x *= x;
  }
  return res;
}

#ifndef ATCODER_MATH_HPP
#define ATCODER_MATH_HPP 1

#include <algorithm>
#include <cassert>
#include <tuple>
#include <vector>
#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1

#include <utility>

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
  x %= m;
  if (x < 0)
    x += m;
  return x;
}

// Fast moduler by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
  unsigned int _m;
  unsigned long long im;

  // @param m `1 <= m`
  barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

  // @return m
  unsigned int umod() const { return _m; }

  // @param a `0 <= a < m`
  // @param b `0 <= b < m`
  // @return `a * b % m`
  unsigned int mul(unsigned int a, unsigned int b) const {
    // [1] m = 1
    // a = b = im = 0, so okay

    // [2] m >= 2
    // im = ceil(2^64 / m)
    // -> im * m = 2^64 + r (0 <= r < m)
    // let z = a*b = c*m + d (0 <= c, d < m)
    // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
    // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) <
    // 2^64 * 2
    // ((ab * im) >> 64) == c or c + 1
    unsigned long long z = a;
    z *= b;
#ifdef _MSC_VER
    unsigned long long x;
    _umul128(z, im, &x);
#else
    unsigned long long x =
        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
    unsigned int v = (unsigned int)(z - x * _m);
    if (_m <= v)
      v += _m;
    return v;
  }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
  if (m == 1)
    return 0;
  unsigned int _m = (unsigned int)(m);
  unsigned long long r = 1;
  unsigned long long y = safe_mod(x, m);
  while (n) {
    if (n & 1)
      r = (r * y) % _m;
    y = (y * y) % _m;
    n >>= 1;
  }
  return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
  if (n <= 1)
    return false;
  if (n == 2 || n == 7 || n == 61)
    return true;
  if (n % 2 == 0)
    return false;
  long long d = n - 1;
  while (d % 2 == 0)
    d /= 2;
  for (long long a : {2, 7, 61}) {
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
  a = safe_mod(a, b);
  if (a == 0)
    return {b, 0};

  // Contracts:
  // [1] s - m0 * a = 0 (mod b)
  // [2] t - m1 * a = 0 (mod b)
  // [3] s * |m1| + t * |m0| <= b
  long long s = b, t = a;
  long long m0 = 0, m1 = 1;

  while (t) {
    long long u = s / t;
    s -= t * u;
    m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b

    // [3]:
    // (s - t * u) * |m1| + t * |m0 - m1 * u|
    // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
    // = s * |m1| + t * |m0| <= b

    auto tmp = s;
    s = t;
    t = tmp;
    tmp = m0;
    m0 = m1;
    m1 = tmp;
  }
  // by [3]: |m0| <= b/g
  // by g != b: |m0| < b/g
  if (m0 < 0)
    m0 += b / s;
  return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
  if (m == 2)
    return 1;
  if (m == 167772161)
    return 3;
  if (m == 469762049)
    return 3;
  if (m == 754974721)
    return 11;
  if (m == 998244353)
    return 3;
  int divs[20] = {};
  divs[0] = 2;
  int cnt = 1;
  int x = (m - 1) / 2;
  while (x % 2 == 0)
    x /= 2;
  for (int i = 3; (long long)(i)*i <= x; i += 2) {
    if (x % i == 0) {
      divs[cnt++] = i;
      while (x % i == 0) {
        x /= i;
      }
    }
  }
  if (x > 1) {
    divs[cnt++] = x;
  }
  for (int g = 2;; g++) {
    bool ok = true;
    for (int i = 0; i < cnt; i++) {
      if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
        ok = false;
        break;
      }
    }
    if (ok)
      return g;
  }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

} // namespace internal

} // namespace atcoder

#endif // ATCODER_INTERNAL_MATH_HPP

namespace atcoder {

long long pow_mod(long long x, long long n, int m) {
  assert(0 <= n && 1 <= m);
  if (m == 1)
    return 0;
  internal::barrett bt((unsigned int)(m));
  unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
  while (n) {
    if (n & 1)
      r = bt.mul(r, y);
    y = bt.mul(y, y);
    n >>= 1;
  }
  return r;
}

long long inv_mod(long long x, long long m) {
  assert(1 <= m);
  auto z = internal::inv_gcd(x, m);
  assert(z.first == 1);
  return z.second;
}

// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long> &r,
                                    const std::vector<long long> &m) {
  assert(r.size() == m.size());
  int n = int(r.size());
  // Contracts: 0 <= r0 < m0
  long long r0 = 0, m0 = 1;
  for (int i = 0; i < n; i++) {
    assert(1 <= m[i]);
    long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
    if (m0 < m1) {
      std::swap(r0, r1);
      std::swap(m0, m1);
    }
    if (m0 % m1 == 0) {
      if (r0 % m1 != r1)
        return {0, 0};
      continue;
    }
    // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)

    // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
    // r2 % m0 = r0
    // r2 % m1 = r1
    // -> (r0 + x*m0) % m1 = r1
    // -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1)
    // -> x = (r1 - r0) / g * inv(u0) (mod u1)

    // im = inv(u0) (mod u1) (0 <= im < u1)
    long long g, im;
    std::tie(g, im) = internal::inv_gcd(m0, m1);

    long long u1 = (m1 / g);
    // |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
    if ((r1 - r0) % g)
      return {0, 0};

    // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
    long long x = (r1 - r0) / g % u1 * im % u1;

    // |r0| + |m0 * x|
    // < m0 + m0 * (u1 - 1)
    // = m0 + m0 * m1 / g - m0
    // = lcm(m0, m1)
    r0 += x * m0;
    m0 *= u1; // -> lcm(m0, m1)
    if (r0 < 0)
      r0 += m0;
  }
  return {r0, m0};
}

long long floor_sum(long long n, long long m, long long a, long long b) {
  long long ans = 0;
  if (a >= m) {
    ans += (n - 1) * n * (a / m) / 2;
    a %= m;
  }
  if (b >= m) {
    ans += n * (b / m);
    b %= m;
  }

  long long y_max = (a * n + b) / m, x_max = (y_max * m - b);
  if (y_max == 0)
    return ans;
  ans += (n - (x_max + a - 1) / a) * y_max;
  ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
  return ans;
}

} // namespace atcoder

#endif // ATCODER_MATH_HPP

using namespace atcoder;
class BSumIsMultiple {
public:
  void solve(std::istream &cin, std::ostream &cout, std::ostream &cerr) {
    ll N;
    cin >> N;
    N *= 2;
    auto factors = factorize(N);
    int n = SZ(factors);
    VI b(n);
    {
      int i = 0;
      for (auto [x, a] : factors) {
        b[i++] = power(x, a);
      }
    }
    ll ans = N - 1;
    if (N == 1)
      BYE(1);
    if (n == 1) {
      BYE(b[0] - 1);
    }
    REP(mask, BIT(n)) {
      ll p = 1, q = 1;
      REP(i, n) if (mask & BIT(i)) p *= b[i];
      else q *= b[i];
      ll b = inv_mod(q, p);
      DBG(p, q, b)
      if (p == 1 || q == 1)
        continue;
      if (b * q > 1 && (b * q - 1) / p > 0)
        chmin(ans, b * q - 1);
    }
    print(ans);
  }
};

#undef int
int main() {

  BSumIsMultiple solver;
  std::istream &in(std::cin);
  std::ostream &out(std::cout);
  std::ostringstream err;
  in.tie(0);
  ios::sync_with_stdio(0);
  solver.solve(in, out, err);
  return 0;
}