結果

問題 No.3333 Consecutive Power Sum (Large)
コンテスト
ユーザー KumaTachiRen
提出日時 2025-11-02 23:19:56
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 11,050 bytes
コンパイル時間 3,981 ms
コンパイル使用メモリ 316,268 KB
実行使用メモリ 95,808 KB
最終ジャッジ日時 2025-11-02 23:20:39
合計ジャッジ時間 42,981 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 57 WA * 6
権限があれば一括ダウンロードができます

ソースコード

diff #
raw source code 

#line 2 "library/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "library/template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "library/template/template.hpp"

#line 2 "library/template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <class T, class S = T>
S SUM(const vector<T> &a) {
  return accumulate(ALL(a), S(0));
}
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;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "library/template/template.hpp"

#line 2 "library/template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

istream& operator>>(istream& is, __uint128_t& x) {
  string s;
  is >> s;
  x = 0;
  for (auto c : s) x = x * 10 + (c - '0');
  return is;
}
ostream& operator<<(ostream& os, const __uint128_t& x) {
  int buf[39];
  buf[0] = 0;
  int k = x == 0;
  for (auto y = x; y > 0; y /= 10) buf[k++] = int(y % 10);
  while (k > 0) os << buf[--k];
  return os;
}
istream& operator>>(istream& is, __int128_t& x) {
  string s;
  is >> s;
  auto it = s.begin();
  bool nega = *it == '-';
  if (nega) it++;
  x = 0;
  for (; it < s.end(); it++) x = x * 10 + (*it - '0');
  if (nega) x = -x;
  return is;
}
ostream& operator<<(ostream& os, const __int128_t& x) {
  if (x < 0) os << '-';
  int buf[39];
  buf[0] = 0;
  int k = x == 0;
  for (auto y = x < 0 ? -x : x; y > 0; y /= 10) buf[k++] = int(y % 10);
  while (k > 0) os << buf[--k];
  return os;
}

template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
  for (auto& v : a) is >> v;
  return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
  cin >> t;
  in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}
#line 10 "library/template/template.hpp"

#line 2 "library/template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int i, T name) {
  cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
  for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
  cerr << ":" << b << " ";
  _show(i + 1, a, c...);
}
#line 2 "main.cpp"

#line 2 "library/util/random.hpp"

namespace Random {
mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
uint64_t get() { return gen(); }
template <class T>
T get(T n) { return get() % n; }
template <class T>
T get(T l, T r) { return get(r - l) % (r - l + 1) + l; }
double uniform() { return double(get(1 << 30)) / (1 << 30); }

template <class T>
vector<T> get_vector(size_t n, T l, T r) {
  vector<T> a(n);
  for (auto& v : a) v = get(l, r);
  return a;
}

template <class Iter>
void shuffle(Iter begin, Iter end) {
  if (begin == end) return;
  int n = end - begin;
  for (int i = n - 1; i > 0; i--) {
    int j = get(i + 1);
    if (j < i) swap(*(begin + i), *(begin + j));
  }
}
};  // namespace Random

/**
 * @brief Random
 */
#line 4 "main.cpp"

u128 pow(u128 x, int n) {
  u128 y = 1;
  while (n) {
    if (n & 1) y *= x;
    x *= x;
    n /= 2;
  }
  return y;
}

u128 sqrt128(u128 n) {
  u128 l = 0, r = u128(1) << 62;
  while (r - l > 1) {
    u128 x = (l + r) / 2;
    (x * x <= n ? l : r) = x;
  }
  return l;
}

// m <= 2^80
u128 mul(u128 x, u128 y, u128 m) {
  const int B = 40;
  const u128 M = (u128(1) << B) - 1;
  u128 x2 = x >> (B * 2);
  u128 x1 = (x >> B) & M;
  u128 x0 = x & M;
  u128 y2 = y >> (B * 2);
  u128 y1 = (y >> B) & M;
  u128 y0 = y & M;
  u128 z = x2 * y2 % m;
  z = ((z << B) + x1 * y2 + x2 * y1) % m;
  z = ((z << B) + x0 * y2 + x1 * y1 + x2 * y0) % m;
  z = ((z << B) + x0 * y1 + x1 * y0) % m;
  z = ((z << B) + x0 * y0) % m;
  return z;
}

u128 modpow(u128 a, u128 n, u128 p) {
  a %= p;
  u128 ret = 1 % p;
  while (n > 0) {
    if (n % 2 == 1) ret = mul(ret, a, p);
    a = mul(a, a, p);
    n /= 2;
  }
  return ret;
}

u128 gcd(u128 x, u128 y) {
  while (y != 0) x %= y, swap(x, y);
  return x;
}

namespace fast_factorize {
bool miller_rabin(const u128& n, vector<u128> ws) {
  if (n <= 2) return n == 2;
  if (n % 2 == 0) return false;
  u128 d = n - 1;
  while (d % 2 == 0) d /= 2;
  for (auto w : ws) {
    if (w % n == 0) continue;
    u128 t = d;
    u128 y = modpow(w, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) y = mul(y, y, n), t *= 2;
    if (y != n - 1 && t % 2 == 0) return false;
  }
  return true;
}

bool miller_rabin_large(u128 n) {
  return miller_rabin(n, {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41});
}

bool is_prime(u128 n) {
  if (n <= 2) return n == 2;
  if (n % 2 == 0) return false;
  return miller_rabin_large(n);
}

u128 pollard_rho(u128 n) {
  if (~n & 1) return 2;
  if (is_prime(n)) return n;
  const int B = 60;
  const u128 M = (u128(1) << B) - 1;
  u128 R;
  auto f = [&](u128 x) -> u128 { return (mul(x, x, n) + R) % n; };
  auto rnd_ = [&]() -> u128 {
    u128 z = (u128(Random::get()) << 64) | u128(Random::get());
    return z % (n - 2) + 2;
  };
  int counter = 0;
  while (1) {
    u128 x, y, ys, q = 1;
    R = rnd_(), y = rnd_();
    u128 g = 1;
    constexpr int m = 128;
    for (int r = 1; g == 1; r <<= 1) {
      x = y;
      for (int i = 0; i < r; ++i) y = f(y);
      for (int k = 0; g == 1 && k < r; k += m) {
        ys = y;
        for (int i = 0; i < m && i < r - k; ++i) q = mul(q, x + n - (y = f(y)), n);
        g = gcd(q, n);
      }
    }
    if (g == n) {
      do
        g = gcd(x + n - (ys = f(ys)), n);
      while (g == 1);
    }
    if (g != n) return g;
  }
  exit(1);
}

vector<u128> inner_factorize(u128 n) {
  if (n <= 1) return {};
  u128 p = pollard_rho(n);
  if (p == n) return {u128(p)};
  auto l = inner_factorize(p);
  auto r = inner_factorize(n / p);
  copy(begin(r), end(r), back_inserter(l));
  return l;
}

vector<u128> factorize(u128 n) {
  auto ret = inner_factorize(n);
  sort(begin(ret), end(ret));
  return ret;
}

map<u128, u128> factor_count(u128 n) {
  map<u128, u128> mp;
  for (auto& x : factorize(n)) mp[x]++;
  return mp;
}

vector<u128> divisors(u128 n) {
  if (n == 0) return {};
  vector<pair<u128, u128>> v;
  for (auto& p : factorize(n)) {
    if (v.empty() || v.back().first != p) {
      v.emplace_back(p, 1);
    } else {
      v.back().second++;
    }
  }
  vector<u128> ret;
  auto f = [&](auto rc, int i, u128 x) -> void {
    if (i == (int)v.size()) {
      ret.push_back(x);
      return;
    }
    rc(rc, i + 1, x);
    for (int j = 0; j < v[i].second; j++) rc(rc, i + 1, x *= v[i].first);
  };
  f(f, 0, 1);
  sort(begin(ret), end(ret));
  return ret;
}

}  // namespace fast_factorize

using fast_factorize::divisors;
using fast_factorize::factor_count;
using fast_factorize::factorize;
// https://nyaannyaan.github.io/library/prime/fast-factorize.hpp
// https://nyaannyaan.github.io/library/prime/miller-rabin.hpp

int main() {
  u128 n;
  in(n);

  vector<tuple<int, u128, u128>> ans;
  for (int e = 1; (u128(1) << e) <= n; e++) {
    if (e == 1) {
      // (r-l+1)(l+r)/2=n
      auto ds = divisors(2 * n);
      for (auto d : ds) {
        // r-l+1=d
        // l+r=2*n/d
        u128 d1 = 2 * n / d;
        if ((d & 1) == (d1 & 1)) continue;
        if (d >= d1) continue;
        u128 l = (d1 - d + 1) / 2;
        u128 r = (d1 + d - 1) / 2;
        ans.push_back({e, l, r});
      }
      sort(ALL(ans));
    } else if (e == 2) {
      // (r-l+1)(2r^2+2lr+2l^2+r-l)=6*n
      auto ds = divisors(12 * n);
      // x=l+r,y=r-l
      // (y+1)(3x^2+y^2+2y)=12*n
      for (auto d : ds) {
        if (12 * n / d / d / d == 0) continue;
        auto y = d - 1;
        // 3x^2+y^2+2y
        auto x = y * y + 2 * y;
        if (x > 12 * n / d) continue;
        x = 12 * n / d - x;
        if (x % 3 != 0) continue;
        x /= 3;
        auto sq = sqrt128(x);
        if (sq * sq != x) continue;
        x = sq;
        if ((x & 1) != (y & 1)) continue;
        auto l = (x - y) / 2;
        auto r = (x + y) / 2;
        ans.push_back({e, l, r});
      }
      sort(ALL(ans));
    } else if (e == 3) {
      auto ds = divisors(4 * n);
      for (auto d : ds) {
        if (d > n / d) continue;
        // r(r+1)-l(l-1)=d
        // r(r+1)+l(l-1)=n/d
        if ((d & 1) != ((n / d) & 1)) continue;
        auto l1 = (n / d - d) / 2;
        auto r1 = (n / d + d) / 2;
        auto l = sqrt128(4 * l1 + 1) / 2;
        auto r = sqrt128(4 * r1 + 1) / 2;
        if (l * (l - 1) == l1 && r * (r + 1) == r1) ans.push_back({e, l, r});
      }
      sort(ALL(ans));
    } else {
      map<u128, int> mp;
      mp[0] = 0;
      u128 s = 0;
      for (int x = 1;; x++) {
        u128 m = n;
        rep(i, 0, e) m /= x;
        if (m == 0) break;
        s += pow(u128(x), e);
        if (mp.contains(s - n)) {
          ans.push_back({e, mp[s - n] + 1, x});
        }
        mp[s] = x;
      }
    }
  }
  out(ans.size());
  for (auto [e, l, r] : ans) out(e, l, r);
}
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