結果
| 問題 | No.3669 误差绝不允许 |
| コンテスト | |
| ユーザー |
👑  みうね
|
| 提出日時 | 2026-08-13 01:29:42 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0) |
| 結果 |
AC
|
| 実行時間 | 564 ms / 3,000 ms |
| + 490µs | |
| コード長 | 52,509 bytes |
| 記録 | |
| コンパイル時間 | 4,262 ms |
| コンパイル使用メモリ | 364,600 KB |
| 実行使用メモリ | 24,772 KB |
| 最終ジャッジ日時 | 2026-09-04 22:24:40 |
| 合計ジャッジ時間 | 12,736 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge3_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 30 |
ソースコード
// BEGIN: ../sakumon/gosayurusanai/main.cpp
#line 1 "..::sakumon::gosayurusanai::main.cpp"
// BEGIN: pch.hpp
#line 3 "pch.hpp"
#if defined(__GNUC__) && !defined(__clang__)
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#define dump(...)
#define CPP_DUMP_SET_OPTION(...)
#define CPP_DUMP_DEFINE_EXPORT_OBJECT(...)
#define CPP_DUMP_DEFINE_EXPORT_ENUM(...)
#define CPP_DUMP_DEFINE_DANGEROUS_EXPORT_OBJECT(...)
// BEGIN: template.hpp
#line 3 "template.hpp"
#include <algorithm>
#include <any>
#include <array>
#include <atomic>
#include <barrier>
#include <bit>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cerrno>
#include <cfenv>
#include <cfloat>
#include <charconv>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <clocale>
#include <cmath>
#include <codecvt>
#include <compare>
#include <complex>
#include <concepts>
#include <condition_variable>
#include <coroutine>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstring>
#include <ctime>
#include <cuchar>
#include <cwchar>
#include <cwctype>
#include <deque>
#include <exception>
#include <execution>
#include <filesystem>
#include <format>
#include <forward_list>
#include <fstream>
#include <functional>
#include <future>
#include <iomanip>
#include <initializer_list>
#include <iostream>
#include <ios>
#include <iosfwd>
#include <istream>
#include <iterator>
#include <latch>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <memory_resource>
#include <mutex>
#include <new>
#include <numbers>
#include <numeric>
#include <optional>
#include <ostream>
#include <queue>
#include <random>
#include <ranges>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <semaphore>
#include <set>
#include <shared_mutex>
#include <source_location>
#include <span>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <stop_token>
#include <streambuf>
#include <string>
#include <string_view>
#include <syncstream>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <valarray>
#include <variant>
#include <vector>
#include <version>
// BEGIN: utilities/fast_io.hpp
#line 3 "utilities::fast_io.hpp"
#include <algorithm>
#include <array>
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#include <utility>
#include <unistd.h>
namespace m1une {
namespace utilities {
namespace internal {
// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};
template <class T>
struct is_range<T, std::void_t<
decltype(std::begin(std::declval<T&>())),
decltype(std::end(std::declval<T&>()))
>> : std::true_type {};
template <class T>
inline constexpr bool is_range_v = is_range<T>::value;
template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));
template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;
template <class T, class = void>
struct range_stored_value {
using type = range_value_t<T>;
};
template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};
template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;
// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};
template <class T, std::size_t N>
struct is_char_array<T[N]>
: std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};
template <class T>
struct is_string_like
: std::bool_constant<
std::is_same_v<std::decay_t<T>, std::string>
|| std::is_same_v<std::decay_t<T>, const char*>
|| std::is_same_v<std::decay_t<T>, char*>
|| is_char_array<std::remove_reference_t<T>>::value
> {};
template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;
// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};
template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
: std::true_type {};
template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;
template <class T, class = void>
struct has_static_mod_raw : std::false_type {};
template <class T>
struct has_static_mod_raw<
T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
: std::true_type {};
template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;
// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
std::is_integral_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>
|| std::is_same_v<std::remove_cv_t<T>, __uint128_t>;
template <class T>
inline constexpr bool is_signed_v =
std::is_signed_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>;
template <class T>
struct make_unsigned {
using type = std::make_unsigned_t<T>;
};
template <>
struct make_unsigned<__int128_t> {
using type = __uint128_t;
};
template <>
struct make_unsigned<__uint128_t> {
using type = __uint128_t;
};
template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;
} // namespace internal
struct FastInput {
static constexpr int buffer_size = 1 << 20;
private:
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _length;
int _file_descriptor;
bool _streaming;
bool refill() {
_position = 0;
if (_streaming) {
ssize_t length;
do {
length = ::read(_file_descriptor, _buffer, buffer_size);
} while (length < 0 && errno == EINTR);
if (length <= 0) {
_length = 0;
return false;
}
_length = int(length);
} else {
_length = int(std::fread(_buffer, 1, buffer_size, _stream));
}
return _length != 0;
}
template <class T>
bool read_integer_from_stream(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-') {
negative = true;
c = read_char_raw();
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
result = negative ? result * 10 - (c - '0')
: result * 10 + (c - '0');
c = read_char_raw();
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + T(c - '0');
c = read_char_raw();
}
value = negative ? T(0) - result : result;
}
return true;
}
bool prepare_number() {
if (_length - _position >= 64) return true;
const int remaining = _length - _position;
if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
_position = 0;
_length = remaining + added;
if (_length < buffer_size) _buffer[_length] = '\0';
return _length != 0;
}
public:
explicit FastInput(std::FILE* stream = stdin)
: _stream(stream),
_position(0),
_length(0),
_file_descriptor(::fileno(stream)),
_streaming([&] {
struct stat status;
return _file_descriptor >= 0
&& ::fstat(_file_descriptor, &status) == 0
&& !S_ISREG(status.st_mode);
}()) {}
FastInput(const FastInput&) = delete;
FastInput& operator=(const FastInput&) = delete;
int read_char_raw() {
if (_position == _length && !refill()) return EOF;
return _buffer[_position++];
}
bool skip_spaces() {
int c = read_char_raw();
while (c != EOF && c <= ' ') c = read_char_raw();
if (c == EOF) return false;
--_position;
return true;
}
bool read(char& value) {
if (!skip_spaces()) return false;
value = char(read_char_raw());
return true;
}
bool read(std::string& value) {
if (!skip_spaces()) return false;
value.clear();
while (true) {
const int begin = _position;
while (_position < _length &&
static_cast<unsigned char>(_buffer[_position]) > ' ') {
++_position;
}
value.append(_buffer + begin, _position - begin);
if (_position < _length) {
++_position;
return true;
}
if (!refill()) return true;
}
}
bool read(bool& value) {
int x;
if (!read(x)) return false;
value = x != 0;
return true;
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>,
bool
>
read(T& value) {
if (_streaming) return read_integer_from_stream(value);
if (!prepare_number()) return false;
int c = static_cast<unsigned char>(_buffer[_position++]);
while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);
bool negative = false;
if (c == '-') {
negative = true;
c = static_cast<unsigned char>(_buffer[_position++]);
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
const int first = c - '0';
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = negative ? result * 100 - (first * 10 + second)
: result * 100 + (first * 10 + second);
++_position;
} else {
result = negative ? result * 10 - first : result * 10 + first;
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
const unsigned first = unsigned(c - '0');
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = result * 100 + T(first * 10 + unsigned(second));
++_position;
} else {
result = result * 10 + T(first);
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = negative ? T(0) - result : result;
}
if (_position > _length) _position = _length;
return true;
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>, bool>
read(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-' || c == '+') {
negative = c == '-';
c = read_char_raw();
}
long double result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + (c - '0');
c = read_char_raw();
}
if (c == '.') {
long double place = 0.1L;
c = read_char_raw();
while ('0' <= c && c <= '9') {
result += (c - '0') * place;
place *= 0.1L;
c = read_char_raw();
}
}
if (c == 'e' || c == 'E') {
c = read_char_raw();
bool exponent_negative = false;
if (c == '-' || c == '+') {
exponent_negative = c == '-';
c = read_char_raw();
}
int exponent = 0;
while ('0' <= c && c <= '9') {
exponent = exponent * 10 + (c - '0');
c = read_char_raw();
}
long double scale = 1;
long double power = 10;
while (exponent > 0) {
if (exponent & 1) scale *= power;
power *= power;
exponent >>= 1;
}
result = exponent_negative ? result / scale : result * scale;
}
value = static_cast<T>(negative ? -result : result);
return true;
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>,
bool
>
read(T& value) {
long long x;
if (!read(x)) return false;
if constexpr (internal::has_static_mod_raw_v<T>) {
if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
value = T::raw(uint32_t(x));
} else {
value = T(x);
}
} else {
value = T(x);
}
return true;
}
template <class First, class Second>
bool read(std::pair<First, Second>& value) {
if (!read(value.first)) return false;
return read(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>,
bool
>
read(Range& range) {
using StoredValue = internal::range_stored_value_t<Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
for (auto&& value : range) {
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
bool x;
if (!read(x)) return false;
value = x;
} else {
if (!read(value)) return false;
}
}
return true;
}
template <class First, class Second, class... Rest>
bool read(First& first, Second& second, Rest&... rest) {
if (!read(first)) return false;
return read(second, rest...);
}
template <class T>
FastInput& operator>>(T& value) {
if (!read(value)) std::abort();
return *this;
}
};
struct FastOutput {
static constexpr int buffer_size = 1 << 20;
private:
inline static const auto digit_quads = [] {
std::array<char, 40000> result{};
for (int i = 0; i < 10000; i++) {
int value = i;
for (int j = 3; j >= 0; j--) {
result[4 * i + j] = char('0' + value % 10);
value /= 10;
}
}
return result;
}();
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _precision;
std::chars_format _float_format;
char _range_separator;
public:
explicit FastOutput(std::FILE* stream = stdout)
: _stream(stream),
_position(0),
_precision(6),
_float_format(std::chars_format::general),
_range_separator(' ') {}
FastOutput(const FastOutput&) = delete;
FastOutput& operator=(const FastOutput&) = delete;
~FastOutput() {
flush();
}
void flush() {
if (_position != 0) {
std::fwrite(_buffer, 1, _position, _stream);
_position = 0;
}
std::fflush(_stream);
}
void write_char(char c) {
if (_position == buffer_size) flush();
_buffer[_position++] = c;
}
void write(const char* s) {
while (*s != '\0') write_char(*s++);
}
void write(const std::string& s) {
std::size_t position = 0;
while (position < s.size()) {
if (_position == buffer_size) flush();
const std::size_t copied =
std::min<std::size_t>(buffer_size - _position, s.size() - position);
std::memcpy(_buffer + _position, s.data() + position, copied);
_position += int(copied);
position += copied;
}
}
void write(char c) {
write_char(c);
}
void write(bool value) {
write_char(value ? '1' : '0');
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>>
write(T value) {
char digits[128];
auto [end, error] = std::to_chars(
digits,
digits + sizeof(digits),
value,
_float_format,
_precision
);
if (error != std::errc()) std::abort();
for (const char* pointer = digits; pointer != end; pointer++) {
write_char(*pointer);
}
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>
>
write(T value) {
using Raw = std::remove_cv_t<T>;
using Unsigned = internal::make_unsigned_t<Raw>;
Unsigned magnitude;
if constexpr (internal::is_signed_v<Raw>) {
if (value < 0) {
write_char('-');
magnitude = Unsigned(0) - Unsigned(value);
} else {
magnitude = Unsigned(value);
}
} else {
magnitude = value;
}
if (magnitude == 0) {
write_char('0');
return;
}
unsigned chunks[16];
int count = 0;
while (magnitude >= 10000) {
const Unsigned quotient = magnitude / 10000;
chunks[count++] = unsigned(magnitude - quotient * 10000);
magnitude = quotient;
}
if (_position > buffer_size - 64) flush();
const unsigned leading = unsigned(magnitude);
const char* first = digit_quads.data() + 4 * leading;
int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
for (; skip < 4; skip++) _buffer[_position++] = first[skip];
while (count--) {
const char* digits = digit_quads.data() + 4 * chunks[count];
std::memcpy(_buffer + _position, digits, 4);
_position += 4;
}
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>
>
write(const T& value) {
write(value.val());
}
template <class First, class Second>
void write(const std::pair<First, Second>& value) {
write(value.first);
write_char(' ');
write(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>
>
write(const Range& range) {
using StoredValue = internal::range_stored_value_t<const Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
bool first = true;
for (const auto& value : range) {
if (!first) write_char(nested ? '\n' : _range_separator);
first = false;
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
write(static_cast<bool>(value));
} else {
write(value);
}
}
}
template <class First, class... Rest>
void print(const First& first, const Rest&... rest) {
write(first);
((write_char(' '), write(rest)), ...);
}
void println() {
write_char('\n');
}
void set_precision(int precision) {
_precision = precision;
}
void set_fixed(int precision = 6) {
_float_format = std::chars_format::fixed;
_precision = precision;
}
void set_general(int precision = 6) {
_float_format = std::chars_format::general;
_precision = precision;
}
void set_range_separator(char separator) {
_range_separator = separator;
}
template <class... Args>
void println(const Args&... args) {
print(args...);
write_char('\n');
}
template <class T>
FastOutput& operator<<(const T& value) {
write(value);
return *this;
}
};
} // namespace utilities
} // namespace m1une
// END: utilities/fast_io.hpp
#line 103 "template.hpp"
using namespace std;
namespace m1une {
namespace template_io {
inline utilities::FastInput& input() {
static utilities::FastInput instance;
return instance;
}
inline utilities::FastOutput& output() {
static utilities::FastOutput instance;
return instance;
}
} // namespace template_io
} // namespace m1une
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
#ifdef __SIZEOF_FLOAT128__
using f128 = __float128;
#endif
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using vi = vector<int>;
using vl = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
using vvi = vvc<int>;
using vvl = vvc<ll>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pqg = std::priority_queue<T, vector<T>, greater<T>>;
template <class T, class U>
using umap = unordered_map<T, U>;
// template <typename K>
// using tree = __gnu_pbds::tree<K, __gnu_pbds::null_type, std::less<>,
// __gnu_pbds::rb_tree_tag,
// __gnu_pbds::tree_order_statistics_node_update>;
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
// FOR(a) := for (ll _ = 0; _ < (ll)a; ++_)
// FOR(i, a) := for (ll i = 0; i < (ll)a; ++i)
// FOR(i, a, b) := for (ll i = a; i < (ll)b; ++i)
// FOR(i, a, b, c) := for (ll i = a; i < (ll)b; i += (c))
// FOR_R(a) := for (ll i = (a) - 1; i >= 0; --i)
// FOR_R(i, a) := for (ll i = (a) - 1; i >= 0; --i)
// FOR_R(i, a, b) := for (ll i = (b) - 1; i >= (ll)a; --i)
#define FOR1(a) for (ll _ = 0; _ < (ll)a; ++_)
#define FOR2(i, a) for (ll i = 0; i < (ll)a; ++i)
#define FOR3(i, a, b) for (ll i = a; i < (ll)b; ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < (ll)b; i += (c))
#define FOR1_R(a) for (ll i = (a) - 1; i >= 0; --i)
#define FOR2_R(i, a) for (ll i = (a) - 1; i >= 0; --i)
#define FOR3_R(i, a, b) for (ll i = (b) - 1; i >= (ll)a; --i)
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FORI1(a) for (int _ = 0; _ < (int)a; ++_)
#define FORI2(i, a) for (int i = 0; i < (int)a; ++i)
#define FORI3(i, a, b) for (int i = a; i < (int)b; ++i)
#define FORI4(i, a, b, c) for (int i = a; i < (int)b; i += (c))
#define FORI1_R(a) for (int i = (a) - 1; i >= 0; --i)
#define FORI2_R(i, a) for (int i = (a) - 1; i >= 0; --i)
#define FORI3_R(i, a, b) for (int i = (b) - 1; i >= (int)a; --i)
#define FORI(...) overload4(__VA_ARGS__, FORI4, FORI3, FORI2, FORI1)(__VA_ARGS__)
#define FORI_R(...) overload3(__VA_ARGS__, FORI3_R, FORI2_R, FORI1_R)(__VA_ARGS__)
#define FOR_subset(t, s) for (int t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
int popcnt(int x) {
return __builtin_popcount(x);
}
int popcnt(u32 x) {
return __builtin_popcount(x);
}
int popcnt(ll x) {
return __builtin_popcountll(x);
}
int popcnt(u64 x) {
return __builtin_popcountll(x);
}
int popcnt_mod_2(int x) {
return __builtin_parity(x);
}
int popcnt_mod_2(u32 x) {
return __builtin_parity(x);
}
int popcnt_mod_2(ll x) {
return __builtin_parityll(x);
}
int popcnt_mod_2(u64 x) {
return __builtin_parityll(x);
}
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) {
return (x == 0 ? -1 : 31 - __builtin_clz(x));
}
int topbit(u32 x) {
return (x == 0 ? -1 : 31 - __builtin_clz(x));
}
int topbit(ll x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
int topbit(u64 x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) {
return (x == 0 ? -1 : __builtin_ctz(x));
}
int lowbit(u32 x) {
return (x == 0 ? -1 : __builtin_ctz(x));
}
int lowbit(ll x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
int lowbit(u64 x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T POW(U x_, int n) {
T x = x_;
T ret = 1;
while (n > 0) {
if (n & 1) ret *= x;
x *= x;
n >>= 1;
}
return ret;
}
template <typename T, typename U>
T SUM(const vector<U>& A) {
T sm = 0;
for (auto&& a : A) sm += a;
return sm;
}
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <class T, class S>
inline bool chmax(T& a, const S& b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T& a, const S& b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string& S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) {
A[i] = (S[i] != '?' ? S[i] - first_char : -1);
}
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U>& A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) {
B[i + 1] = B[i] + A[i];
}
if (off == 0) B.erase(B.begin());
return B;
}
template <typename T>
vector<int> argsort(const vector<T>& A) {
vector<int> ids(A.size());
iota(all(ids), 0);
sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T>& A, const vc<int>& I) {
vc<T> B(I.size());
FOR(i, I.size()) B[i] = A[I[i]];
return B;
}
template <class... T>
constexpr auto min(T... a) {
return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T>
constexpr auto max(T... a) {
return max(initializer_list<common_type_t<T...>>{a...});
}
template <class... Ts>
bool scan(Ts&... values) {
return m1une::template_io::input().read(values...);
}
template <class... Ts>
void print(const Ts&... values) {
m1une::template_io::output().println(values...);
}
void YESNO(bool b) {
m1une::template_io::output().println(b ? "YES" : "NO");
}
void YesNo(bool b) {
m1une::template_io::output().println(b ? "Yes" : "No");
}
void YES() {
m1une::template_io::output().println("YES");
}
void NO() {
m1une::template_io::output().println("NO");
}
void Yes() {
m1une::template_io::output().println("Yes");
}
void No() {
m1une::template_io::output().println("No");
}
// END: template.hpp
#line 29 "pch.hpp"
// END: pch.hpp
#line 2 "..::sakumon::gosayurusanai::main.cpp"
// BEGIN: graph/dijkstra.hpp
#line 3 "graph::dijkstra.hpp"
#include <algorithm>
#include <cassert>
#include <queue>
#include <utility>
#include <vector>
// BEGIN: graph.hpp
#line 3 "graph.hpp"
#include <cassert>
#include <utility>
#include <vector>
namespace m1une {
namespace graph {
template <class T = int>
struct Edge {
using cost_type = T;
int from;
int to;
T cost;
int id;
bool alive;
Edge() : from(-1), to(-1), cost(T()), id(-1), alive(true) {}
Edge(int from_, int to_, T cost_ = T(1), int id_ = -1, bool alive_ = true)
: from(from_), to(to_), cost(cost_), id(id_), alive(alive_) {}
int other(int v) const {
assert(v == from || v == to);
return from ^ to ^ v;
}
};
template <class T = int>
struct Graph {
using edge_type = Edge<T>;
using cost_type = T;
private:
int _n;
int _edge_count;
std::vector<std::vector<edge_type>> _g;
std::vector<std::vector<std::pair<int, int>>> _edge_positions;
public:
Graph() : _n(0), _edge_count(0) {}
explicit Graph(int n) : _n(n), _edge_count(0), _g(n) {
assert(0 <= n);
}
int size() const {
return _n;
}
bool empty() const {
return _n == 0;
}
int edge_count() const {
return _edge_count;
}
int add_vertex() {
_g.emplace_back();
return _n++;
}
int add_directed_edge(int from, int to, T cost = T(1)) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
int id = _edge_count++;
int idx = int(_g[from].size());
_g[from].push_back(edge_type(from, to, cost, id));
_edge_positions.emplace_back();
_edge_positions.back().push_back({from, idx});
return id;
}
int add_edge(int u, int v, T cost = T(1)) {
assert(0 <= u && u < _n);
assert(0 <= v && v < _n);
int id = _edge_count++;
int u_idx = int(_g[u].size());
_g[u].push_back(edge_type(u, v, cost, id));
int v_idx = int(_g[v].size());
_g[v].push_back(edge_type(v, u, cost, id));
_edge_positions.emplace_back();
_edge_positions.back().push_back({u, u_idx});
_edge_positions.back().push_back({v, v_idx});
return id;
}
void set_edge_alive(int id, bool alive) {
assert(0 <= id && id < _edge_count);
for (auto [v, idx] : _edge_positions[id]) {
_g[v][idx].alive = alive;
}
}
void erase_edge(int id) {
set_edge_alive(id, false);
}
void revive_edge(int id) {
set_edge_alive(id, true);
}
bool is_edge_alive(int id) const {
assert(0 <= id && id < _edge_count);
assert(!_edge_positions[id].empty());
auto [v, idx] = _edge_positions[id][0];
return _g[v][idx].alive;
}
const std::vector<edge_type>& operator[](int v) const {
assert(0 <= v && v < _n);
return _g[v];
}
std::vector<edge_type>& operator[](int v) {
assert(0 <= v && v < _n);
return _g[v];
}
const std::vector<std::vector<edge_type>>& adjacency() const {
return _g;
}
std::vector<std::vector<edge_type>>& adjacency() {
return _g;
}
std::vector<edge_type> edges(bool include_inactive = false) const {
std::vector<edge_type> result;
result.reserve(_edge_count);
std::vector<char> used(_edge_count, false);
for (int v = 0; v < _n; v++) {
for (const auto& e : _g[v]) {
if (!include_inactive && !e.alive) continue;
if (0 <= e.id && e.id < _edge_count) {
if (used[e.id]) continue;
used[e.id] = true;
}
result.push_back(e);
}
}
return result;
}
Graph reversed() const {
Graph result(_n);
result._edge_count = _edge_count;
result._edge_positions.assign(_edge_count, {});
for (int v = 0; v < _n; v++) {
for (const auto& e : _g[v]) {
int idx = int(result._g[e.to].size());
result._g[e.to].push_back(edge_type(e.to, e.from, e.cost, e.id, e.alive));
if (0 <= e.id && e.id < _edge_count) result._edge_positions[e.id].push_back({e.to, idx});
}
}
return result;
}
};
} // namespace graph
} // namespace m1une
// END: graph.hpp
#line 11 "graph::dijkstra.hpp"
namespace m1une {
namespace graph {
template <class T>
struct DijkstraResult {
std::vector<T> dist;
std::vector<char> reached;
std::vector<int> parent;
std::vector<int> parent_edge;
T inf = T();
bool reachable(int v) const {
assert(0 <= v && v < int(dist.size()));
return reached[v];
}
std::vector<int> path(int t) const {
assert(reachable(t));
std::vector<int> result;
for (int v = t; v != -1; v = parent[v]) result.push_back(v);
std::reverse(result.begin(), result.end());
return result;
}
};
namespace internal {
template <class T>
struct DijkstraQueueNode {
T dist;
int vertex;
};
template <class T>
struct DijkstraQueueCompare {
bool operator()(const DijkstraQueueNode<T>& first,
const DijkstraQueueNode<T>& second) const {
return second.dist < first.dist;
}
};
} // namespace internal
template <class T>
DijkstraResult<T> dijkstra(const Graph<T>& g,
const std::vector<int>& sources) {
int n = g.size();
DijkstraResult<T> result;
result.dist.resize(n);
result.reached.assign(n, false);
result.parent.assign(n, -1);
result.parent_edge.assign(n, -1);
using Node = internal::DijkstraQueueNode<T>;
using Compare = internal::DijkstraQueueCompare<T>;
std::priority_queue<Node, std::vector<Node>, Compare> que;
for (int s : sources) {
assert(0 <= s && s < n);
if (result.reached[s]) continue;
result.reached[s] = true;
result.dist[s] = T();
que.push(Node{T(), s});
}
while (!que.empty()) {
Node current = que.top();
que.pop();
if (result.dist[current.vertex] < current.dist) continue;
for (const auto& e : g[current.vertex]) {
if (!e.alive) continue;
T nd = current.dist + e.cost;
if (result.reached[e.to] && !(nd < result.dist[e.to])) continue;
result.reached[e.to] = true;
result.dist[e.to] = nd;
result.parent[e.to] = current.vertex;
result.parent_edge[e.to] = e.id;
que.push(Node{std::move(nd), e.to});
}
}
return result;
}
template <class T>
DijkstraResult<T> dijkstra(const Graph<T>& g, int s) {
return dijkstra(g, std::vector<int>{s});
}
// Compatibility overload: unreachable distances are replaced by inf after the
// search. Reachability itself never depends on this sentinel.
template <class T>
DijkstraResult<T> dijkstra(const Graph<T>& g,
const std::vector<int>& sources, const T& inf) {
DijkstraResult<T> result = dijkstra(g, sources);
result.inf = inf;
for (int v = 0; v < int(result.dist.size()); v++) {
if (!result.reachable(v)) result.dist[v] = inf;
}
return result;
}
template <class T>
DijkstraResult<T> dijkstra(const Graph<T>& g, int s, const T& inf) {
return dijkstra(g, std::vector<int>{s}, inf);
}
} // namespace graph
} // namespace m1une
// END: graph/dijkstra.hpp
#line 3 "..::sakumon::gosayurusanai::main.cpp"
// BEGIN: utilities/int512.hpp
#line 3 "utilities::int512.hpp"
#include <string>
#include <string_view>
// BEGIN: detail/fixed_int.hpp
#line 3 "detail::fixed_int.hpp"
#include <algorithm>
#include <array>
#include <concepts>
#include <cstddef>
#include <cstdint>
#include <istream>
#include <ostream>
#include <stdexcept>
#include <string>
#include <string_view>
#include <type_traits>
#include <utility>
namespace m1une {
namespace utilities {
namespace detail {
// A signed two's-complement integer whose arithmetic wraps modulo 2^Bits.
// Public aliases select contest-friendly fixed widths in int*.hpp.
template <std::size_t Bits>
class FixedInt {
static_assert(Bits >= 64);
static_assert(Bits % 64 == 0);
private:
static constexpr std::size_t limb_count = Bits / 64;
using LimbArray = std::array<std::uint64_t, limb_count>;
public:
static constexpr std::size_t bit_width = Bits;
constexpr FixedInt() = default;
template <std::integral Integer>
constexpr FixedInt(Integer value) {
static_assert(sizeof(Integer) <= sizeof(std::uint64_t));
if constexpr (std::signed_integral<Integer>) {
const std::uint64_t extension =
value < 0 ? ~std::uint64_t(0) : std::uint64_t(0);
limbs_.fill(extension);
limbs_[0] = static_cast<std::uint64_t>(
static_cast<std::int64_t>(value)
);
} else {
limbs_[0] = static_cast<std::uint64_t>(value);
}
}
explicit FixedInt(std::string_view text) { read(text); }
FixedInt& operator=(std::string_view text) {
read(text);
return *this;
}
void read(std::string_view text) {
if (text.empty()) {
throw std::invalid_argument("empty fixed-width integer");
}
const bool negative = text.front() == '-';
std::size_t position =
(text.front() == '-' || text.front() == '+') ? 1 : 0;
if (position == text.size()) {
throw std::invalid_argument("invalid fixed-width integer");
}
FixedInt result;
for (; position < text.size(); ++position) {
const char digit = text[position];
if (digit < '0' || digit > '9') {
throw std::invalid_argument("invalid fixed-width integer");
}
result.multiply_unsigned_small(10);
result += FixedInt(static_cast<unsigned>(digit - '0'));
}
*this = negative ? -result : result;
}
constexpr bool is_zero() const {
for (const std::uint64_t limb : limbs_) {
if (limb != 0) return false;
}
return true;
}
constexpr bool is_negative() const {
return (limbs_.back() >> 63) != 0;
}
constexpr int sign() const {
if (is_zero()) return 0;
return is_negative() ? -1 : 1;
}
constexpr FixedInt operator+() const { return *this; }
constexpr FixedInt operator-() const {
FixedInt result;
result.limbs_ = limbs_;
negate_unsigned(result.limbs_);
return result;
}
constexpr FixedInt& operator+=(const FixedInt& other) {
__uint128_t carry = 0;
for (std::size_t index = 0; index < limb_count; ++index) {
const __uint128_t current =
__uint128_t(limbs_[index]) + other.limbs_[index] + carry;
limbs_[index] = static_cast<std::uint64_t>(current);
carry = current >> 64;
}
return *this;
}
constexpr FixedInt& operator-=(const FixedInt& other) {
return *this += -other;
}
constexpr FixedInt& operator*=(const FixedInt& other) {
LimbArray product{};
for (std::size_t first = 0; first < limb_count; ++first) {
__uint128_t carry = 0;
for (
std::size_t second = 0;
first + second < limb_count;
++second
) {
const std::size_t position = first + second;
const __uint128_t current =
__uint128_t(limbs_[first]) * other.limbs_[second] +
product[position] + carry;
product[position] = static_cast<std::uint64_t>(current);
carry = current >> 64;
}
}
limbs_ = product;
return *this;
}
constexpr FixedInt& multiply_small(std::uint64_t value) {
multiply_unsigned_small(value);
return *this;
}
constexpr FixedInt& operator/=(const FixedInt& other) {
return *this = divmod(*this, other).first;
}
constexpr FixedInt& operator%=(const FixedInt& other) {
return *this = divmod(*this, other).second;
}
std::string to_string() const {
if (is_zero()) return "0";
const bool negative = is_negative();
LimbArray magnitude = unsigned_magnitude();
std::string result;
while (!magnitude_is_zero(magnitude)) {
const unsigned digit = divide_unsigned_by_ten(magnitude);
result.push_back(static_cast<char>('0' + digit));
}
if (negative) result.push_back('-');
std::reverse(result.begin(), result.end());
return result;
}
friend constexpr std::pair<FixedInt, FixedInt> divmod(
const FixedInt& dividend,
const FixedInt& divisor
) {
if (divisor.is_zero()) {
throw std::domain_error("fixed-width integer division by zero");
}
const bool quotient_negative =
dividend.is_negative() != divisor.is_negative();
const bool remainder_negative = dividend.is_negative();
auto [quotient_limbs, remainder_limbs] = divide_unsigned(
dividend.unsigned_magnitude(), divisor.unsigned_magnitude()
);
FixedInt quotient;
FixedInt remainder;
quotient.limbs_ = quotient_limbs;
remainder.limbs_ = remainder_limbs;
if (quotient_negative) quotient = -quotient;
if (remainder_negative) remainder = -remainder;
return std::make_pair(quotient, remainder);
}
friend constexpr std::pair<FixedInt, std::int64_t> divmod_small(
const FixedInt& dividend,
std::uint32_t divisor
) {
if (divisor == 0) {
throw std::domain_error("fixed-width integer division by zero");
}
LimbArray quotient_limbs = dividend.unsigned_magnitude();
const std::uint64_t unsigned_remainder =
divide_unsigned_by_small(quotient_limbs, divisor);
FixedInt quotient;
quotient.limbs_ = quotient_limbs;
if (dividend.is_negative()) quotient = -quotient;
const std::int64_t remainder = dividend.is_negative()
? -std::int64_t(unsigned_remainder)
: std::int64_t(unsigned_remainder);
return std::make_pair(quotient, remainder);
}
friend constexpr FixedInt operator+(
FixedInt first,
const FixedInt& second
) {
return first += second;
}
friend constexpr FixedInt operator-(
FixedInt first,
const FixedInt& second
) {
return first -= second;
}
friend constexpr FixedInt operator*(
FixedInt first,
const FixedInt& second
) {
return first *= second;
}
friend constexpr FixedInt operator/(
FixedInt first,
const FixedInt& second
) {
return first /= second;
}
friend constexpr FixedInt operator%(
FixedInt first,
const FixedInt& second
) {
return first %= second;
}
friend constexpr bool operator==(
const FixedInt& first,
const FixedInt& second
) = default;
friend constexpr bool operator<(
const FixedInt& first,
const FixedInt& second
) {
const bool first_negative = first.is_negative();
const bool second_negative = second.is_negative();
if (first_negative != second_negative) return first_negative;
return compare_unsigned(first.limbs_, second.limbs_) < 0;
}
friend constexpr bool operator!=(
const FixedInt& first,
const FixedInt& second
) {
return !(first == second);
}
friend constexpr bool operator>(
const FixedInt& first,
const FixedInt& second
) {
return second < first;
}
friend constexpr bool operator<=(
const FixedInt& first,
const FixedInt& second
) {
return !(second < first);
}
friend constexpr bool operator>=(
const FixedInt& first,
const FixedInt& second
) {
return !(first < second);
}
friend std::ostream& operator<<(
std::ostream& output,
const FixedInt& value
) {
return output << value.to_string();
}
friend std::istream& operator>>(
std::istream& input,
FixedInt& value
) {
std::string text;
if (input >> text) value.read(text);
return input;
}
private:
LimbArray limbs_{};
constexpr LimbArray unsigned_magnitude() const {
LimbArray result = limbs_;
if (is_negative()) negate_unsigned(result);
return result;
}
constexpr void multiply_unsigned_small(std::uint64_t value) {
__uint128_t carry = 0;
for (std::size_t index = 0; index < limb_count; ++index) {
const __uint128_t current =
__uint128_t(limbs_[index]) * value + carry;
limbs_[index] = static_cast<std::uint64_t>(current);
carry = current >> 64;
}
}
static constexpr void negate_unsigned(LimbArray& value) {
for (std::uint64_t& limb : value) limb = ~limb;
for (std::size_t index = 0; index < limb_count; ++index) {
if (++value[index] != 0) break;
}
}
static constexpr int compare_unsigned(
const LimbArray& first,
const LimbArray& second
) {
for (std::size_t offset = 0; offset < limb_count; ++offset) {
const std::size_t index = limb_count - 1 - offset;
if (first[index] != second[index]) {
return first[index] < second[index] ? -1 : 1;
}
}
return 0;
}
static constexpr void subtract_unsigned(
LimbArray& first,
const LimbArray& second
) {
std::uint64_t borrow = 0;
for (std::size_t index = 0; index < limb_count; ++index) {
const std::uint64_t previous = first[index];
first[index] -= second[index] + borrow;
const bool addition_overflow =
borrow != 0 && second[index] == ~std::uint64_t(0);
borrow = addition_overflow ||
previous < second[index] + borrow;
}
}
static constexpr void shift_left_one(LimbArray& value) {
std::uint64_t carry = 0;
for (std::size_t index = 0; index < limb_count; ++index) {
const std::uint64_t next_carry = value[index] >> 63;
value[index] = (value[index] << 1) | carry;
carry = next_carry;
}
}
static constexpr std::pair<LimbArray, LimbArray> divide_unsigned(
const LimbArray& dividend,
const LimbArray& divisor
) {
LimbArray quotient{};
LimbArray remainder{};
for (std::size_t offset = 0; offset < Bits; ++offset) {
const std::size_t bit = Bits - 1 - offset;
shift_left_one(remainder);
remainder[0] |=
(dividend[bit / 64] >> (bit % 64)) & std::uint64_t(1);
if (compare_unsigned(remainder, divisor) >= 0) {
subtract_unsigned(remainder, divisor);
quotient[bit / 64] |= std::uint64_t(1) << (bit % 64);
}
}
return std::make_pair(quotient, remainder);
}
static bool magnitude_is_zero(const LimbArray& value) {
for (const std::uint64_t limb : value) {
if (limb != 0) return false;
}
return true;
}
static constexpr std::uint64_t divide_unsigned_by_small(
LimbArray& value,
std::uint64_t divisor
) {
__uint128_t remainder = 0;
for (std::size_t offset = 0; offset < limb_count; ++offset) {
const std::size_t index = limb_count - 1 - offset;
const __uint128_t current =
(remainder << 64) | value[index];
value[index] = static_cast<std::uint64_t>(current / divisor);
remainder = current % divisor;
}
return static_cast<std::uint64_t>(remainder);
}
static unsigned divide_unsigned_by_ten(LimbArray& value) {
return static_cast<unsigned>(divide_unsigned_by_small(value, 10));
}
};
} // namespace detail
} // namespace utilities
} // namespace m1une
// END: detail/fixed_int.hpp
#line 8 "utilities::int512.hpp"
namespace m1une {
namespace utilities {
using Int512 = detail::FixedInt<512>;
using i512 = Int512;
inline Int512 parse_int512(std::string_view text) {
return Int512(text);
}
inline std::string to_string(const Int512& value) {
return value.to_string();
}
} // namespace utilities
} // namespace m1une
// END: utilities/int512.hpp
#line 4 "..::sakumon::gosayurusanai::main.cpp"
auto& fastin = m1une::template_io::input();
auto& fastout = m1une::template_io::output();
using Int512 = m1une::utilities::Int512;
std::vector<std::pair<int, int>> prime_powers() {
std::vector<std::pair<int, int>> result;
std::array<bool, 301> composite{};
for (int p = 2; p <= 300; ++p) {
if (composite[p]) continue;
for (int multiple = p + p; multiple <= 300; multiple += p) {
composite[multiple] = true;
}
int exponent = 0;
int power = 1;
while (power <= 300 / p) {
power *= p;
++exponent;
}
result.emplace_back(p, exponent);
}
return result;
}
void solve() {
const std::vector<std::pair<int, int>> factors = prime_powers();
Int512 common_denominator = 1;
for (auto [prime, exponent] : factors) {
for (int i = 0; i < exponent; ++i) {
common_denominator.multiply_small(prime);
}
}
std::array<Int512, 301> scale;
for (int denominator = 1; denominator <= 300; ++denominator) {
auto [quotient, remainder] =
divmod_small(common_denominator, denominator);
assert(remainder == 0);
scale[denominator] = quotient;
}
int N, M;
scan(N, M);
m1une::graph::Graph<Int512> graph(N);
while (M--) {
int u, v, a, b;
scan(u, v, a, b);
--u;
--v;
Int512 cost = scale[b];
cost.multiply_small(a);
graph.add_edge(u, v, cost);
}
const auto shortest = m1une::graph::dijkstra(graph, 0);
for (int v = 1; v < N; ++v) {
Int512 numerator = shortest.dist[v];
Int512 denominator = 1;
for (auto [prime, exponent] : factors) {
int removed = 0;
while (removed < exponent) {
auto [quotient, remainder] = divmod_small(numerator, prime);
if (remainder != 0) break;
numerator = quotient;
++removed;
}
for (int i = removed; i < exponent; ++i) {
denominator.multiply_small(prime);
}
}
print(numerator.to_string(), denominator.to_string());
}
}
int main() {
int T = 1;
while (T--) solve();
return 0;
}
// END: ../sakumon/gosayurusanai/main.cpp