#line 1 "verify/verify-yosupo-math/yosupo-stern-brocot-tree-2.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/stern_brocot_tree"
//
#line 2 "template/template.hpp"
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(T &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // namespace Nyaan
#line 58 "template/template.hpp"
// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
#line 61 "template/template.hpp"
// inout
#line 1 "template/inout.hpp"
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
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...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
#line 64 "template/template.hpp"
// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t t) {
if (t == 0) cerr << 0;
if (t < 0) cerr << '-', t = -t;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
void dump(__uint128_t t) {
if (t == 0) cerr << 0;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
cerr << " ";
dump(head);
if (sizeof...(tail) != 0) cerr << ",";
trace(std::forward<Tail>(tail)...);
}
} // namespace DebugImpl
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"
// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
#line 70 "template/template.hpp"
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-yosupo-math/yosupo-stern-brocot-tree-2.test.cpp"
//
#line 2 "math/rational.hpp"
#line 6 "math/rational.hpp"
using namespace std;
#line 2 "internal/internal-type-traits.hpp"
#line 4 "internal/internal-type-traits.hpp"
using namespace std;
namespace internal {
template <typename T>
using is_broadly_integral =
typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
is_same_v<T, __uint128_t>,
true_type, false_type>::type;
template <typename T>
using is_broadly_signed =
typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
true_type, false_type>::type;
template <typename T>
using is_broadly_unsigned =
typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
true_type, false_type>::type;
#define ENABLE_VALUE(x) \
template <typename T> \
constexpr bool x##_v = x<T>::value;
ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE
#define ENABLE_HAS_TYPE(var) \
template <class, class = void> \
struct has_##var : false_type {}; \
template <class T> \
struct has_##var<T, void_t<typename T::var>> : true_type {}; \
template <class T> \
constexpr auto has_##var##_v = has_##var<T>::value;
#define ENABLE_HAS_VAR(var) \
template <class, class = void> \
struct has_##var : false_type {}; \
template <class T> \
struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
template <class T> \
constexpr auto has_##var##_v = has_##var<T>::value;
} // namespace internal
#line 2 "math-fast/gcd.hpp"
#line 4 "math-fast/gcd.hpp"
using namespace std;
namespace BinaryGCDImpl {
using u64 = unsigned long long;
using i8 = char;
u64 binary_gcd(u64 a, u64 b) {
if (a == 0 || b == 0) return a + b;
i8 n = __builtin_ctzll(a);
i8 m = __builtin_ctzll(b);
a >>= n;
b >>= m;
n = min(n, m);
while (a != b) {
u64 d = a - b;
i8 s = __builtin_ctzll(d);
bool f = a > b;
b = f ? b : a;
a = (f ? d : -d) >> s;
}
return a << n;
}
using u128 = __uint128_t;
// a > 0
int ctz128(u128 a) {
u64 lo = a & u64(-1);
return lo ? __builtin_ctzll(lo) : 64 + __builtin_ctzll(a >> 64);
}
u128 binary_gcd128(u128 a, u128 b) {
if (a == 0 || b == 0) return a + b;
i8 n = ctz128(a);
i8 m = ctz128(b);
a >>= n;
b >>= m;
n = min(n, m);
while (a != b) {
u128 d = a - b;
i8 s = ctz128(d);
bool f = a > b;
b = f ? b : a;
a = (f ? d : -d) >> s;
}
return a << n;
}
} // namespace BinaryGCDImpl
long long binary_gcd(long long a, long long b) {
return BinaryGCDImpl::binary_gcd(abs(a), abs(b));
}
__int128_t binary_gcd128(__int128_t a, __int128_t b) {
if (a < 0) a = -a;
if (b < 0) b = -b;
return BinaryGCDImpl::binary_gcd128(a, b);
}
/**
* @brief binary GCD
*/
#line 10 "math/rational.hpp"
// T : 値, U : 比較用
template <typename T, typename U>
struct RationalBase {
using R = RationalBase;
using Key = T;
T x, y;
RationalBase() : x(0), y(1) {}
template <typename T1>
RationalBase(const T1& _x) : RationalBase<T, U>(_x, T1{1}) {}
template <typename T1, typename T2>
RationalBase(const pair<T1, T2>& _p)
: RationalBase<T, U>(_p.first, _p.second) {}
template <typename T1, typename T2>
RationalBase(const T1& _x, const T2& _y) : x(_x), y(_y) {
assert(y != 0);
if (y == -1) x = -x, y = -y;
if (y != 1) {
T g;
if constexpr (internal::is_broadly_integral_v<T>) {
if constexpr (sizeof(T) == 16) {
g = binary_gcd128(x, y);
} else {
g = binary_gcd(x, y);
}
} else {
g = gcd(x, y);
}
if (g != 0) x /= g, y /= g;
if (y < 0) x = -x, y = -y;
}
}
// y = 0 の代入も認める
static R raw(T _x, T _y) {
R r;
r.x = _x, r.y = _y;
return r;
}
friend R operator+(const R& l, const R& r) {
if (l.y == r.y) return R{l.x + r.x, l.y};
return R{l.x * r.y + l.y * r.x, l.y * r.y};
}
friend R operator-(const R& l, const R& r) {
if (l.y == r.y) return R{l.x - r.x, l.y};
return R{l.x * r.y - l.y * r.x, l.y * r.y};
}
friend R operator*(const R& l, const R& r) { return R{l.x * r.x, l.y * r.y}; }
friend R operator/(const R& l, const R& r) { return R{l.x * r.y, l.y * r.x}; }
R& operator+=(const R& r) { return (*this) = (*this) + r; }
R& operator-=(const R& r) { return (*this) = (*this) - r; }
R& operator*=(const R& r) { return (*this) = (*this) * r; }
R& operator/=(const R& r) { return (*this) = (*this) / r; }
R operator-() const { return raw(-x, y); }
R inverse() const {
assert(x != 0);
R r = raw(y, x);
if (r.y < 0) r.x = -r.x, r.y = -r.y;
return r;
}
R pow(long long p) const {
R res{1}, base{*this};
while (p) {
if (p & 1) res *= base;
base *= base;
p >>= 1;
}
return res;
}
friend bool operator==(const R& l, const R& r) {
return l.x == r.x && l.y == r.y;
};
friend bool operator!=(const R& l, const R& r) {
return l.x != r.x || l.y != r.y;
};
friend bool operator<(const R& l, const R& r) {
return U{l.x} * r.y < U{l.y} * r.x;
};
friend bool operator<=(const R& l, const R& r) { return l < r || l == r; }
friend bool operator>(const R& l, const R& r) {
return U{l.x} * r.y > U{l.y} * r.x;
};
friend bool operator>=(const R& l, const R& r) { return l > r || l == r; }
friend ostream& operator<<(ostream& os, const R& r) {
os << r.x;
if (r.x != 0 && r.y != 1) os << "/" << r.y;
return os;
}
// T にキャストされるので T が bigint の場合は to_ll も要る
T to_mint(T mod) const {
assert(mod != 0);
T a = y, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return U((u % mod + mod) % mod) * x % mod;
}
};
using Rational = RationalBase<long long, __int128_t>;
using Fraction = Rational;
#line 2 "math/stern-brocot-tree-binary-search.hpp"
#line 5 "math/stern-brocot-tree-binary-search.hpp"
using namespace std;
#line 2 "math/stern-brocot-tree.hpp"
#line 6 "math/stern-brocot-tree.hpp"
using namespace std;
// x / y (x > 0, y > 0) を管理、デフォルトで 1 / 1
// 入力が互いに素でない場合は gcd を取って格納
// seq : (1, 1) から (x, y) へのパス。右の子が正/左の子が負
template <typename Int>
struct SternBrocotTreeNode {
using Node = SternBrocotTreeNode;
Int lx, ly, x, y, rx, ry;
vector<Int> seq;
SternBrocotTreeNode() : lx(0), ly(1), x(1), y(1), rx(1), ry(0) {}
SternBrocotTreeNode(Int X, Int Y) : SternBrocotTreeNode() {
assert(1 <= X && 1 <= Y);
Int g = gcd(X, Y);
X /= g, Y /= g;
while (min(X, Y) > 0) {
if (X > Y) {
Int d = X / Y;
X -= d * Y;
go_right(d - (X == 0 ? 1 : 0));
} else {
Int d = Y / X;
Y -= d * X;
go_left(d - (Y == 0 ? 1 : 0));
}
}
}
SternBrocotTreeNode(const pair<Int, Int> &xy)
: SternBrocotTreeNode(xy.first, xy.second) {}
SternBrocotTreeNode(const vector<Int> &_seq) : SternBrocotTreeNode() {
for (const Int &d : _seq) {
assert(d != 0);
if (d > 0) go_right(d);
if (d < 0) go_left(d);
}
assert(seq == _seq);
}
// pair<Int, Int> 型で分数を get
pair<Int, Int> get() const { return make_pair(x, y); }
// 区間の下限
pair<Int, Int> lower_bound() const { return make_pair(lx, ly); }
// 区間の上限
pair<Int, Int> upper_bound() const { return make_pair(rx, ry); }
// 根からの深さ
Int depth() const {
Int res = 0;
for (auto &s : seq) res += abs(s);
return res;
}
// 左の子に d 進む
void go_left(Int d = 1) {
if (d <= 0) return;
if (seq.empty() or seq.back() > 0) seq.push_back(0);
seq.back() -= d;
rx += lx * d, ry += ly * d;
x = rx + lx, y = ry + ly;
}
// 右の子に d 進む
void go_right(Int d = 1) {
if (d <= 0) return;
if (seq.empty() or seq.back() < 0) seq.push_back(0);
seq.back() += d;
lx += rx * d, ly += ry * d;
x = rx + lx, y = ry + ly;
}
// 親の方向に d 進む
// d 進めたら true, 進めなかったら false を返す
bool go_parent(Int d = 1) {
if (d <= 0) return true;
while (d != 0) {
if (seq.empty()) return false;
Int d2 = min(d, abs(seq.back()));
if (seq.back() > 0) {
x -= rx * d2, y -= ry * d2;
lx = x - rx, ly = y - ry;
seq.back() -= d2;
} else {
x -= lx * d2, y -= ly * d2;
rx = x - lx, ry = y - ly;
seq.back() += d2;
}
d -= d2;
if (seq.back() == 0) seq.pop_back();
if (d2 == Int{0}) break;
}
return true;
}
// SBT 上の LCA
static Node lca(const Node &lhs, const Node &rhs) {
Node n;
for (int i = 0; i < min<int>(lhs.seq.size(), rhs.seq.size()); i++) {
Int val1 = lhs.seq[i], val2 = rhs.seq[i];
if ((val1 < 0) != (val2 < 0)) break;
if (val1 < 0) n.go_left(min(-val1, -val2));
if (val1 > 0) n.go_right(min(val1, val2));
if (val1 != val2) break;
}
return n;
}
friend ostream &operator<<(ostream &os, const Node &rhs) {
os << "\n";
os << "L : ( " << rhs.lx << ", " << rhs.ly << " )\n";
os << "M : ( " << rhs.x << ", " << rhs.y << " )\n";
os << "R : ( " << rhs.rx << ", " << rhs.ry << " )\n";
os << "seq : {";
for (auto &x : rhs.seq) os << x << ", ";
os << "} \n";
return os;
}
friend bool operator<(const Node &lhs, const Node &rhs) {
return lhs.x * rhs.y < rhs.x * lhs.y;
}
friend bool operator==(const Node &lhs, const Node &rhs) {
return lhs.x == rhs.x and lhs.y == rhs.y;
}
};
/**
* @brief Stern-Brocot Tree
*/
#line 8 "math/stern-brocot-tree-binary-search.hpp"
// 分子と分母が INF 以下である非負の既約分数のうち次のものを返す
// first : f(x) が false である最大の既約分数 x
// second : f(x) が true である最小の既約分数 x
// ただし
// - f(0) = true の場合は (0/1, 0/1) を返す
// - true になる分数が存在しない場合は (?, 1/0) を返す
// - INF = 0 の場合は (0/1, 1/0) を返す
template <typename I>
pair<pair<I, I>, pair<I, I>> binary_search_on_stern_brocot_tree(
function<bool(pair<I, I>)> f, const I &INF) {
// INF >= 0
assert(0 <= INF);
SternBrocotTreeNode<I> m;
if (INF == 0) return {m.lower_bound(), m.upper_bound()};
// INF 条件を超える or f(m) = return_value である
auto over = [&](bool return_value) {
return max(m.x, m.y) > INF or f(m.get()) == return_value;
};
if (f(make_pair(0, 1))) return {m.lower_bound(), m.lower_bound()};
int go_left = over(true);
for (; true; go_left ^= 1) {
if (go_left) {
// f(M) = true -> (L, M] に答えがある
// (f(L * b + M) = false) or (INF 超え) になる b の最小は？
I a = 1;
for (; true; a *= 2) {
m.go_left(a);
if (over(false)) {
m.go_parent(a);
break;
}
}
for (a /= 2; a != 0; a /= 2) {
m.go_left(a);
if (over(false)) m.go_parent(a);
}
m.go_left(1);
if (max(m.get().first, m.get().second) > INF)
return {m.lower_bound(), m.upper_bound()};
} else {
// f(M) = false -> (M, R] に答えがある
// (f(M + R * b) = true) or (INF 超え) になる b の最小は？
I a = 1;
for (; true; a *= 2) {
m.go_right(a);
if (over(true)) {
m.go_parent(a);
break;
}
}
for (a /= 2; a != 0; a /= 2) {
m.go_right(a);
if (over(true)) m.go_parent(a);
}
m.go_right(1);
if (max(m.get().first, m.get().second) > INF)
return {m.lower_bound(), m.upper_bound()};
}
}
}
#line 8 "verify/verify-yosupo-math/yosupo-stern-brocot-tree-2.test.cpp"
using namespace Nyaan;
using SBT = SternBrocotTreeNode<ll>;
void Nyaan::solve() {
int T;
cin >> T;
while (T--) {
ins(cmd);
if (cmd == "DECODE_PATH") {
ini(n);
SBT f;
rep(_, n) {
char c;
in(c);
inl(x);
if (c == 'R') f.go_right(x);
if (c == 'L') f.go_left(x);
}
out(f.x, f.y);
} else if (cmd == "ENCODE_PATH") {
inl(x, y);
SBT f{x, y};
cout << f.seq.size() << " ";
each(s, f.seq) {
cout << (s > 0 ? 'R' : 'L') << " ";
cout << abs(s) << " ";
}
cout << "\n";
} else if (cmd == "LCA") {
inl(x1, y1, x2, y2);
SBT f{x1, y1}, g{x2, y2};
SBT h = SBT::lca(f, g);
out(h.x, h.y);
} else if (cmd == "ANCESTOR") {
inl(k, x, y);
SBT f{x, y};
ll l = f.depth() - k;
if (l < 0) {
out(-1);
} else {
bool b = f.go_parent(l);
assert(b == true);
out(f.x, f.y);
}
} else {
inl(x, y);
auto p = binary_search_on_stern_brocot_tree<ll>(
[&](pair<ll, ll> f) {
return Rational{x, y} <= Rational{f};
},
max(x, y) - 1);
out(p.fi.fi, p.fi.se, p.se.fi, p.se.se);
}
}
}
verify/verify-yosupo-math/yosupo-stern-brocot-tree-2.test.cpp