結果
| 問題 | No.1871 divisXor |
| ユーザー |
 suisen
|
| 提出日時 | 2022-03-11 21:48:12 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 26,501 bytes |
| コンパイル時間 | 2,603 ms |
| コンパイル使用メモリ | 217,992 KB |
| 実行使用メモリ | 4,368 KB |
| 最終ジャッジ日時 | 2023-10-23 19:10:26 |
| 合計ジャッジ時間 | 4,595 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge13 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
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| testcase_01 | AC | 2 ms
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| testcase_02 | AC | 2 ms
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| testcase_03 | AC | 2 ms
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| testcase_04 | AC | 2 ms
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| testcase_05 | AC | 2 ms
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| testcase_06 | AC | 2 ms
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| testcase_07 | AC | 2 ms
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| testcase_08 | AC | 2 ms
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| testcase_09 | AC | 2 ms
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| testcase_10 | AC | 2 ms
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| testcase_11 | AC | 2 ms
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| testcase_12 | AC | 2 ms
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| testcase_13 | AC | 2 ms
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| testcase_14 | AC | 2 ms
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| testcase_15 | AC | 2 ms
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| testcase_16 | AC | 2 ms
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| testcase_17 | AC | 2 ms
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| testcase_18 | AC | 2 ms
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| testcase_19 | AC | 2 ms
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| testcase_20 | AC | 2 ms
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| testcase_21 | AC | 2 ms
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| testcase_22 | AC | 2 ms
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| testcase_23 | AC | 2 ms
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| testcase_24 | AC | 2 ms
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| testcase_25 | AC | 2 ms
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| testcase_26 | AC | 2 ms
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| testcase_27 | AC | 2 ms
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| testcase_28 | AC | 2 ms
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| testcase_29 | AC | 2 ms
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| testcase_30 | AC | 2 ms
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ソースコード
// #pragma comment(linker, "/stack:200000000")
#include <bits/stdc++.h>
#include <limits>
#include <type_traits>
namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
if constexpr (cond_v) {
return std::forward<Then>(then);
} else {
return std::forward<OrElse>(or_else);
}
}
// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;
template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;
// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;
// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;
} // namespace suisen
// ! type aliases
using i128 = __int128_t;
using u128 = __uint128_t;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
template <typename T> using vec = std::vector<T>;
template <typename T> using vec2 = vec<vec <T>>;
template <typename T> using vec3 = vec<vec2<T>>;
template <typename T> using vec4 = vec<vec3<T>>;
template <typename T>
using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T, typename U>
using umap = std::unordered_map<T, U>;
// ! macros (capital: internal macro)
#define OVERLOAD2(_1,_2,name,...) name
#define OVERLOAD3(_1,_2,_3,name,...) name
#define OVERLOAD4(_1,_2,_3,_4,name,...) name
#define REP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define REP3(i,l,r) REP4(i,l,r,1)
#define REP2(i,n) REP3(i,0,n)
#define REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define REPINF2(i,l) REPINF3(i,l,1)
#define REPINF1(i) REPINF2(i,0)
#define RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))
#define RREP3(i,l,r) RREP4(i,l,r,1)
#define RREP2(i,n) RREP3(i,0,n)
#define rep(...) OVERLOAD4(__VA_ARGS__, REP4 , REP3 , REP2 )(__VA_ARGS__)
#define rrep(...) OVERLOAD4(__VA_ARGS__, RREP4 , RREP3 , RREP2 )(__VA_ARGS__)
#define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__)
#define CAT_I(a, b) a##b
#define CAT(a, b) CAT_I(a, b)
#define UNIQVAR(tag) CAT(tag, __LINE__)
#define loop(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;)
#define all(iterable) (iterable).begin(), (iterable).end()
#define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__)
// ! I/O utilities
// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U> &a) {
return out << a.first << ' ' << a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::ostream& operator<<(std::ostream& out, const std::tuple<Args...> &a) {
if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
return out;
} else {
out << std::get<N>(a);
if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) {
out << ' ';
}
return operator<<<N + 1>(out, a);
}
}
// vector
template <typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T> &a) {
for (auto it = a.begin(); it != a.end();) {
out << *it;
if (++it != a.end()) out << ' ';
}
return out;
}
// array
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& out, const std::array<T, N> &a) {
for (auto it = a.begin(); it != a.end();) {
out << *it;
if (++it != a.end()) out << ' ';
}
return out;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head &head, const Tail &...tails) {
std::cout << head;
if (sizeof...(tails)) std::cout << ' ';
print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
for (auto it = v.begin(); it != v.end();) {
std::cout << *it;
if (++it != v.end()) std::cout << sep;
}
std::cout << end;
}
// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U> &a) {
return in >> a.first >> a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::istream& operator>>(std::istream& in, std::tuple<Args...> &a) {
if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
return in;
} else {
return operator>><N + 1>(in >> std::get<N>(a), a);
}
}
// vector
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T> &a) {
for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
return in;
}
// array
template <typename T, size_t N>
std::istream& operator>>(std::istream& in, std::array<T, N> &a) {
for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
return in;
}
template <typename ...Args>
void read(Args &...args) {
( std::cin >> ... >> args );
}
// ! integral utilities
// Returns pow(-1, n)
template <typename T>
constexpr inline int pow_m1(T n) {
return -(n & 1) | 1;
}
// Returns pow(-1, n)
template <>
constexpr inline int pow_m1<bool>(bool n) {
return -int(n) | 1;
}
// Returns floor(x / y)
template <typename T>
constexpr inline T fld(const T x, const T y) {
return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
}
template <typename T>
constexpr inline T cld(const T x, const T y) {
return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
}
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcount(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcount(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcountll(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }
template <typename T>
constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }
template <typename T>
constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); }
template <typename T>
constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }
template <typename T>
constexpr inline int parity(const T x) { return popcount(x) & 1; }
struct all_subset {
struct all_subset_iter {
const int s; int t;
constexpr all_subset_iter(int s) : s(s), t(s + 1) {}
constexpr auto operator*() const { return t; }
constexpr auto operator++() {}
constexpr auto operator!=(std::nullptr_t) { return t ? (--t &= s, true) : false; }
};
int s;
constexpr all_subset(int s) : s(s) {}
constexpr auto begin() { return all_subset_iter(s); }
constexpr auto end() { return nullptr; }
};
// ! container
template <typename T, typename Comparator, suisen::constraints_t<suisen::is_comparator<Comparator, T>> = nullptr>
auto priqueue_comp(const Comparator comparator) {
return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}
template <typename Iterable>
auto isize(const Iterable &iterable) -> decltype(int(iterable.size())) {
return iterable.size();
}
template <typename T, typename Gen, suisen::constraints_t<suisen::is_same_as_invoke_result<T, Gen, int>> = nullptr>
auto generate_vector(int n, Gen generator) {
std::vector<T> v(n);
for (int i = 0; i < n; ++i) v[i] = generator(i);
return v;
}
template <typename T>
auto generate_range_vector(T l, T r) {
return generate_vector(r - l, [l](int i) { return l + i; });
}
template <typename T>
auto generate_range_vector(T n) {
return generate_range_vector(0, n);
}
template <typename T>
void sort_unique_erase(std::vector<T> &a) {
std::sort(a.begin(), a.end());
a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <typename InputIterator, typename BiConsumer>
auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {
if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);
}
template <typename Container, typename BiConsumer>
auto foreach_adjacent_values(Container c, BiConsumer f) -> decltype(c.begin(), c.end(), void()){
foreach_adjacent_values(c.begin(), c.end(), f);
}
// ! other utilities
// x <- min(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmin(T &x, const T &y) {
if (y >= x) return false;
x = y;
return true;
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T &x, const T &y) {
if (y <= x) return false;
x = y;
return true;
}
namespace suisen {}
using namespace suisen;
using namespace std;
struct io_setup {
io_setup(int precision = 20) {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(precision);
}
} io_setup_ {};
// ! code from here
#include <cmath>
#include <iostream>
#include <random>
#include <numeric>
#include <cassert>
#include <cstdint>
#include <iterator>
namespace suisen::miller_rabin {
namespace internal {
constexpr uint32_t THRESHOLD_1 = 341531U;
constexpr uint64_t BASE_1[] { 9345883071009581737ULL };
constexpr uint32_t THRESHOLD_2 = 1050535501U;
constexpr uint64_t BASE_2[] { 336781006125ULL, 9639812373923155ULL };
constexpr uint64_t THRESHOLD_3 = 350269456337ULL;
constexpr uint64_t BASE_3[] { 4230279247111683200ULL, 14694767155120705706ULL, 16641139526367750375ULL };
constexpr uint64_t THRESHOLD_4 = 55245642489451ULL;
constexpr uint64_t BASE_4[] { 2ULL, 141889084524735ULL, 1199124725622454117ULL, 11096072698276303650ULL };
constexpr uint64_t THRESHOLD_5 = 7999252175582851ULL;
constexpr uint64_t BASE_5[] { 2ULL, 4130806001517ULL, 149795463772692060ULL, 186635894390467037ULL, 3967304179347715805ULL };
constexpr uint64_t THRESHOLD_6 = 585226005592931977ULL;
constexpr uint64_t BASE_6[] { 2ULL, 123635709730000ULL, 9233062284813009ULL, 43835965440333360ULL, 761179012939631437ULL, 1263739024124850375ULL };
constexpr uint32_t BASE_7[] { 2U, 325U, 9375U, 28178U, 450775U, 9780504U, 1795265022U };
template <auto BASE, std::size_t SIZE, typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
bool miller_rabin(T _n) {
using U = std::make_unsigned_t<T>;
using M = safely_multipliable_t<U>;
U n = _n, d = (n - 1) >> __builtin_ctzll(n - 1);
if (n == 2 or n == 3 or n == 5 or n == 7) return true;
if (n % 2 == 0 or n % 3 == 0 or n % 5 == 0 or n % 7 == 0) return false;
for (std::size_t i = 0; i < SIZE; ++i) {
M y = 1, p = BASE[i] % n;
if (p == 0) continue;
for (U d2 = d; d2; d2 >>= 1) {
if (d2 & 1) y = y * p % n;
p = p * p % n;
}
if (y == 1) continue;
for (U t = d; y != n - 1; t <<= 1) {
y = y * y % n;
if (y == 1 or t == n - 1) return false;
}
}
return true;
}
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
bool is_prime(T n) {
if (n <= 1) return false;
using namespace internal;
if (n < THRESHOLD_1) {
return miller_rabin<BASE_1, 1>(n);
} else if (n < THRESHOLD_2) {
return miller_rabin<BASE_2, 2>(n);
} else if (n < THRESHOLD_3) {
return miller_rabin<BASE_3, 3>(n);
} else if (n < THRESHOLD_4) {
return miller_rabin<BASE_4, 4>(n);
} else if (n < THRESHOLD_5) {
return miller_rabin<BASE_5, 5>(n);
} else if (n < THRESHOLD_6) {
return miller_rabin<BASE_6, 6>(n);
} else {
return miller_rabin<BASE_7, 7>(n);
}
}
} // namespace suisen::miller_rabin
namespace suisen::fast_factorize {
namespace internal {
template <typename T>
int floor_log2(T n) {
int i = 0;
while (n) n >>= 1, ++i;
return i - 1;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
T pollard_rho(T n) {
using M = safely_multipliable_t<T>;
const T m = T(1) << (floor_log2(n) / 5);
static std::mt19937_64 rng{std::random_device{}()};
std::uniform_int_distribution<T> dist(0, n - 1);
while (true) {
T c = dist(rng);
auto f = [&](T x) -> T { return (M(x) * x + c) % n; };
T x, y = 2, ys, q = 1, g = 1;
for (T r = 1; g == 1; r <<= 1) {
x = y;
for (T i = 0; i < r; ++i) y = f(y);
for (T k = 0; k < r and g == 1; k += m) {
ys = y;
for (T i = 0; i < std::min(m, r - k); ++i) y = f(y), q = M(q) * (x > y ? x - y : y - x) % n;
g = std::gcd(q, n);
}
}
if (g == n) {
g = 1;
while (g == 1) ys = f(ys), g = std::gcd(x > ys ? x - ys : ys - x, n);
}
if (g < n) {
if (miller_rabin::is_prime(g)) return g;
if (T d = n / g; miller_rabin::is_prime(d)) return d;
return pollard_rho(g);
}
}
}
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<std::pair<T, int>> factorize(T n) {
std::vector<std::pair<T, int>> res;
if ((n & 1) == 0) {
int q = 0;
do ++q, n >>= 1; while ((n & 1) == 0);
res.emplace_back(2, q);
}
for (T p = 3; p * p <= n; p += 2) {
if (p >= 101 and n >= 1 << 20) {
while (n > 1) {
if (miller_rabin::is_prime(n)) {
res.emplace_back(std::exchange(n, 1), 1);
} else {
p = internal::pollard_rho(n);
int q = 0;
do ++q, n /= p; while (n % p == 0);
res.emplace_back(p, q);
}
}
break;
}
if (n % p == 0) {
int q = 0;
do ++q, n /= p; while (n % p == 0);
res.emplace_back(p, q);
}
}
if (n > 1) res.emplace_back(n, 1);
return res;
}
} // namespace suisen::fast_factorize
#include <algorithm>
#include <array>
#include <optional>
#include <tuple>
#include <vector>
namespace suisen {
// // Returns pow(-1, n)
// template <typename T>
// constexpr inline int pow_m1(T n) {
// return -(n & 1) | 1;
// }
// // Returns pow(-1, n)
// template <>
// constexpr inline int pow_m1<bool>(bool n) {
// return -int(n) | 1;
// }
// // Returns floor(x / y)
// template <typename T>
// constexpr inline T fld(const T x, const T y) {
// return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
// }
// // Returns ceil(x / y)
// template <typename T>
// constexpr inline T cld(const T x, const T y) {
// return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
// }
/**
* O(sqrt(n))
* Returns a vector of { prime, index }.
* It is guaranteed that `prime` is ascending.
*/
template <typename T>
std::vector<std::pair<T, int>> factorize(T n) {
static constexpr std::array primes{ 2, 3, 5, 7, 11, 13 };
static constexpr int next_prime = 17;
static constexpr int siz = std::array{ 1, 2, 8, 48, 480, 5760, 92160 } [primes.size() - 1] ;
static constexpr int period = [] {
int res = 1;
for (auto e : primes) res *= e;
return res;
}();
static constexpr struct S : public std::array<int, siz> {
constexpr S() {
for (int i = next_prime, j = 0; i < period + next_prime; i += 2) {
bool ok = true;
for (int p : primes) ok &= i % p > 0;
if (ok) (*this)[j++] = i - next_prime;
}
}
} s{};
assert(n > 0);
std::vector<std::pair<T, int>> res;
auto f = [&res, &n](int p) {
if (n % p) return;
int cnt = 0;
do n /= p, ++cnt; while (n % p == 0);
res.emplace_back(p, cnt);
};
for (int p : primes) f(p);
for (T b = next_prime; b * b <= n; b += period) {
for (int offset : s) f(b + offset);
}
if (n != 1) res.emplace_back(n, 1);
return res;
}
/**
* O(sigma(n))
* Returns a vector that contains all divisors of `n`.
* It is NOT guaranteed that the vector is sorted.
*/
template <typename T>
std::vector<T> divisors(const std::vector<std::pair<T, int>>& factorized) {
std::vector<T> res{ 1 };
for (auto [p, c] : factorized) {
for (int i = 0, sz = res.size(); i < sz; ++i) {
T d = res[i];
for (int j = 0; j < c; ++j) res.push_back(d *= p);
}
}
return res;
}
/**
* O(sqrt(n))
* Returns a vector that contains all divisors of `n`.
* It is NOT guaranteed that the vector is sorted.
*/
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
std::vector<T> divisors(T n) {
return divisors(factorize(n));
}
template <typename T>
T totient(T n) {
for (const auto& [p, _] : factorize(n)) n /= p, n *= p - 1;
return n;
}
// Returns { l, r } := min_max { x>0 | fld(n,x)=q }.
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
std::optional<std::pair<T, T>> same_fld_denominators_positive(T n, T q, T max_val = std::numeric_limits<T>::max()) {
T l, r;
if (q >= 0) {
if (n < 0) return std::nullopt;
// cld(n + 1, q + 1) <= x <= fld(n, q)
l = (n + 1 + q) / (q + 1), r = q == 0 ? max_val : std::min(max_val, n / q);
} else {
if (n >= 0) return std::nullopt;
// cld(n, q) <= x <= fld(n + 1, q + 1)
l = (n + q + 1) / q, r = q == -1 ? max_val : std::min(max_val, (n + 1) / (q + 1));
}
if (l <= r) return std::make_pair(l, r);
else return std::nullopt;
}
// Returns { l, r } := min_max { x<0 | fld(n,x)=q }.
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
std::optional<std::pair<T, T>> same_fld_denominators_negative(T n, T q, T min_val = std::numeric_limits<T>::min()) {
T l, r;
if (q >= 0) {
if (n > 0) return std::nullopt;
// cld(n, q) <= x <= fld(n - 1, q + 1)
l = q == 0 ? min_val : std::max(min_val, n / q), r = (n - 1 - q) / (q + 1);
} else {
if (n <= 0) return std::nullopt;
// cld(n - 1, q + 1) <= x <= fld(n, q)
l = q == -1 ? min_val : std::max(min_val, (n - 1) / (q + 1)), r = (n - q - 1) / q;
}
if (l <= r) return std::make_pair(l, r);
else return std::nullopt;
}
// Returns { l, r } := min_max { x>0 | cld(n,x)=q }.
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
std::optional<std::pair<T, T>> same_cld_denominators_positive(T n, T q, T max_val = std::numeric_limits<T>::max()) {
T l, r;
if (q > 0) {
if (n <= 0) return std::nullopt;
l = (n + q - 1) / q, r = q == 1 ? max_val : std::min(max_val, (n - 1) / (q - 1));
} else {
if (n > 0) return std::nullopt;
l = (n - 1 + q) / (q - 1), r = q == 0 ? max_val : std::min(max_val, n / q);
}
if (l <= r) return std::make_pair(l, r);
else return std::nullopt;
}
// Returns { l, r } := min_max { x<0 | cld(n,x)=q }.
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
std::optional<std::pair<T, T>> same_cld_denominators_negative(T n, T q, T min_val = std::numeric_limits<T>::min()) {
T l, r;
if (q > 0) {
if (n >= 0) return std::nullopt;
l = q == 1 ? min_val : std::max(min_val, (n + 1) / (q - 1)), r = (n - q + 1) / q;
} else {
if (n < 0) return std::nullopt;
l = q == 0 ? min_val : std::max(min_val, n / q), r = (n + 1 - q) / (q - 1);
}
if (l <= r) return std::make_pair(l, r);
else return std::nullopt;
}
/**
* O(sqrt(n)).
* Returns vector of { l : T, r : T, q : T } s.t. let S be { d | n / d = q }, l = min S and r = max S.
* It is guaranteed that `l`, `r` is ascending (i.e. `q` is descending).
*/
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
auto enumerate_quotients(T n) {
assert(0 <= n);
std::vector<std::tuple<T, T, T>> res;
for (T l = 1, r = 1; l <= n; l = r + 1) {
T q = n / l;
res.emplace_back(l, r = n / q, q);
}
return res;
}
/**
* Template Parameter:
* - vector<T> or array<T, N>
*
* Time Complexity: O(|vs| * Sum_{v in vs} sqrt(v))
*
* Returns vector of { l : T, r : T, qs : Container } s.t. let S be { d | vs[i] / d = qs[i] (for all i) }, l = min S and r = max S
* It is guaranteed that `l`, `r` is ascending (i.e. for all `i`, `q[i]` is descending).
*/
template <typename Container>
std::vector<std::tuple<typename Container::value_type, typename Container::value_type, Container>>
enumerate_multiple_quotients(const Container& vs) {
using T = typename Container::value_type;
static_assert(std::is_integral_v<T>);
int n = vs.size();
T max_val = *std::max_element(vs.begin(), vs.end());
assert(*std::min_element(vs.begin(), vs.end()) >= 0);
std::vector<std::tuple<T, T, Container>> res;
for (T l = 1, r = 1; l <= max_val; l = r + 1) {
Container qs;
if constexpr (std::is_same_v<Container, std::vector<T>>) qs.resize(n);
r = std::numeric_limits<T>::max();
for (int i = 0; i < n; ++i) {
qs[i] = vs[i] / l;
r = std::min(r, qs[i] == 0 ? std::numeric_limits<T>::max() : vs[i] / qs[i]);
}
res.emplace_back(l, r, std::move(qs));
}
return res;
}
} // namespace suisen
int main() {
input(long long, n);
if (n == 0) {
print(-1);
return 0;
}
vector<long long> ans;
vector<long long> fs;
while (n) {
long long x = n;
while (true) {
if (x == 0) {
print(ans);
print(n);
return 0;
}
long long div_sum = 1;
for (auto [p, c] : fast_factorize::factorize(x)) {
long long s = 0, q = 1;
loop(c + 1) {
s += q;
q *= p;
}
div_sum *= s;
}
long long n2 = n ^ div_sum;
if (2 * n2 <= n) {
ans.push_back(x);
fs.push_back(div_sum);
n = n2;
break;
}
--x;
}
}
print(ans.size());
print(ans);
// print(fs);
return 0;
}