結果
| 問題 | No.3073 Fraction Median |
| コンテスト | |
| ユーザー |
 miscalc
|
| 提出日時 | 2026-08-07 21:07:04 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.90.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 51,405 bytes |
| 記録 | |
| コンパイル時間 | 3,379 ms |
| コンパイル使用メモリ | 369,820 KB |
| 実行使用メモリ | 38,656 KB |
| 最終ジャッジ日時 | 2026-08-07 21:07:16 |
| 合計ジャッジ時間 | 10,769 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge1_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 3 WA * 15 |
ソースコード
#define INF 4'000'000'000'000'000'037LL
#define EPS 1e-11
#include <bits/stdc++.h>
using namespace std;
using ld = decltype(EPS);
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
using tllll = tuple<ll, ll, ll, ll>;
#define vc vector
template <class T>
using vvc = vc<vc<T>>;
using vpll = vc<pll>;
using vstr = vc<string>;
using i128 = __int128_t;
using u128 = __uint128_t;
i128 stoi128(const string &s)
{
i128 res = 0;
if (s.front() == '-')
{
for (int i = 1; i < (int)s.size(); i++)
res = 10 * res + s[i] - '0';
res = -res;
}
else
{
for (auto &&c : s)
res = 10 * res + c - '0';
}
return res;
}
string i128tos(i128 x)
{
if (x == 0) return "0";
string sign = "", res = "";
if (x < 0)
x = -x, sign = "-";
while (x > 0)
{
res += '0' + x % 10;
x /= 10;
}
reverse(res.begin(), res.end());
return sign + res;
}
istream &operator>>(istream &is, i128 &a)
{
string s;
is >> s;
a = stoi128(s);
return is;
}
ostream &operator<<(ostream &os, const i128 &a)
{
os << i128tos(a);
return os;
}
#define cauto const auto
#define overload4(_1,_2,_3,_4,name,...) name
#define repi1(i,n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi2(i,l,r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)
#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
template <class T>
constexpr bool is_integral_ext = is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>;
template <class T>
constexpr bool is_signed_ext = is_signed_v<T> || is_same_v<T, i128>;
template <class T>
constexpr bool is_unsigned_ext = is_unsigned_v<T> || is_same_v<T, u128>;
template <class T, class U>
inline bool chmin(T &a, U b) { return a > b ? a = b, true : false; }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divround(U a, V b) { return divfloor<T>(2 * T(a) + T(b), 2 * T(b)); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T safemod(U a, V b) { return T(a) - T(b) * divfloor<T>(a, b); }
template <class T = ll, class U, class V>
constexpr T ipow(U a, V b)
{
assert(b >= 0);
if (b == 0)
return 1;
if (a == 0 || a == 1)
return a;
if (a < 0 && a == -1)
return b & 1 ? -1 : 1;
T res = 1, tmp = a;
while (true)
{
if (b & 1)
res *= tmp;
b >>= 1;
if (b == 0)
break;
tmp *= tmp;
}
return res;
}
template <class T = ll, class A, class B, class M>
T mul_limited(A a, B b, M m)
{
assert(a >= 0 && b >= 0 && m >= 0);
if (b == 0)
return 0;
return T(a) > T(m) / T(b) ? T(m) : T(a) * T(b);
}
template <class T = ll, class A, class B>
T mul_limited(A a, B b) { return mul_limited<T>(a, b, INF); }
template <class T = ll, class A, class B, class M>
T pow_limited(A a, B b, M m)
{
assert(a >= 0 && b >= 0 && m >= 0);
if (a <= 1 || b == 0)
return min(ipow<T>(a, b), T(m));
T res = 1, tmp = a;
while (true)
{
if (b & 1)
{
if (res > T(m) / tmp)
return m;
res *= tmp;
}
b >>= 1;
if (b == 0)
break;
if (tmp > T(m) / tmp)
return m;
tmp *= tmp;
}
return res;
}
template <class T = ll, class A, class B>
T pow_limited(A a, B b) { return pow_limited<T>(a, b, INF); }
template <class T = ll, class A, class K>
constexpr T iroot(A a, K k)
{
assert(a >= 0 && k >= 1);
if (a <= 1 || k == 1)
return a;
if (k == 2)
{
if constexpr (sizeof(T) > sizeof(ull))
{
if ((u128)a < ((u128)1 << 120))
return sqrtl(a);
}
else
return sqrtl(a);
}
auto isok = [&](T x) -> bool
{
if (x == 0)
return true;
T res = 1, k2 = k;
while (true)
{
if (k2 & 1)
{
if (res > T(a) / x)
return false;
res *= x;
}
k2 >>= 1;
if (k2 == 0)
break;
if (x > T(a) / x)
return false;
x *= x;
}
return res <= T(a);
};
T x = pow(a, 1.0 / k);
bool up = true;
while (!isok(x))
up = false, x--;
if (up)
{
while (x < numeric_limits<T>::max() && isok(x + 1))
x++;
}
return x;
}
template <class T = ll, class U, class V>
vc<T> base_repr(U val, V base)
{
assert(val >= 0);
assert(base >= 2);
if (val == 0)
return {0};
vc<T> a;
while (val > 0)
{
a.emplace_back(val % base);
val /= base;
}
reverse(a.begin(), a.end());
return a;
}
template <class T = ll, class U, class V>
vc<T> base_repr(U val, V base, int n)
{
assert(val >= 0);
assert(base >= 2);
assert(n >= 0);
vc<T> a(n);
repi(i, n)
{
a[i] = val % base;
val /= base;
}
reverse(a.begin(), a.end());
return a;
}
template <const bool use_upper = true, class U>
string base_repr_str(U val, int base, int n)
{
assert(val >= 0);
assert(2 <= base && base <= 36);
assert(n >= 0);
auto a = base_repr(val, base, n);
string s = "";
for (cauto &ai : a)
s += (ai < 10 ? '0' + ai : (use_upper ? 'A' : 'a') + (ai - 10));
return s;
}
#define ALL(a) (a).begin(), (a).end()
template <class T = ll, class V>
inline T SZ(const V &x) { return x.size(); }
#define eb emplace_back
#define LMD(x,fx) ([&](auto x) { return fx; })
template <class F>
auto gen_vec(int n, const F &f)
{
vc<decltype(f(0))> res(n);
repi(i, n) res[i] = f(i);
return res;
}
template <class T, size_t d, size_t i = 0, class V>
auto dvec(const V (&sz)[d], const T &init)
{
if constexpr (i < d)
return vc(sz[i], dvec<T, d, i + 1>(sz, init));
else
return init;
}
template <class T = ll>
T ctol(const char &c, const string &s)
{
repi(i, SZ<int>(s)) if (s[i] == c) return i;
return -1;
}
template <class T = ll>
vc<T> stov(const string &s, const string &t)
{
return gen_vec(SZ<int>(s), [&](int i) -> T
{ return ctol(s[i], t); });
}
template <class T>
string vtos(const vc<T> &v, const string &t)
{
string res = "";
fe(vi : v) res += t[vi];
return res;
}
template <class T>
vc<T> concat(const vc<T> &v) { return v; }
template <class T, class... Ts>
vc<T> concat(vc<T> v, const vc<Ts> &...vs)
{
(v.insert(v.end(), ALL(vs)), ...);
return v;
}
template <class T, class V>
T SUM(const V &v)
{
T s{};
fec(vi : v) s += vi;
return s;
}
template <class V>
auto MAX(const V &v) { return *max_element(ALL(v)); }
template <class T, class U>
vc<T> permuted(const vc<T> &a, const vc<U> &p)
{
const int n = p.size();
vc<T> res(n);
repi(i, n)
{
assert(0 <= p[i] && p[i] < U(a.size()));
res[i] = a[p[i]];
}
return res;
}
template <class T, class U, class... Ts>
vc<T> permuted(const vc<T> &p, const vc<U> &q, const vc<Ts> &...rs)
{
return permuted(permuted(p, q), rs...);
}
template <class V>
V reversed(const V &v) { return V(v.rbegin(), v.rend()); }
template <class V>
void unique(V &v) { v.erase(std::unique(ALL(v)), v.end()); }
template <class V>
void sortunique(V &v)
{
sort(ALL(v));
unique(v);
}
template <class V, class U>
void rotate(V &v, U k)
{
const U n = v.size();
k = (k % n + n) % n;
std::rotate(v.begin(), v.begin() + k, v.end());
}
template <class T>
vvc<T> top(const vvc<T> &a)
{
if (a.empty())
return {};
const int n = a.size(), m = a[0].size();
vvc<T> b(m, vc<T>(n));
repi(i, n)
{
assert(SZ<int>(a[i]) == m);
repi(j, m) b[j][i] = a[i][j];
}
return b;
}
vstr top(const vstr &a)
{
vvc<char> a_(a.size());
repi(i, SZ<int>(a)) a_[i] = {ALL(a[i])};
vvc<char> b_ = top(a_);
vstr b(b_.size());
repi(i, SZ<int>(b)) b[i] = {ALL(b_[i])};
return b;
}
template <class T, class = void>
struct has_e0 : false_type {};
template <class T>
struct has_e0<T, void_t<decltype(T::e0())>> : true_type {};
template <class T>
inline constexpr bool has_e0_v = has_e0<T>::value;
template <class T>
struct MonoidAdd
{
using S = T;
static constexpr S op(S a, S b) { return a + b; }
static constexpr S e()
{
if constexpr (has_e0_v<S>)
return S::e0();
else
return {};
}
};
template <class T, const T infty = INF>
struct MonoidMin
{
using S = T;
static constexpr S op(S a, S b) { return min(a, b); }
static constexpr S e() { return infty; }
};
template <class T, const T infty = INF>
struct MonoidMax
{
using S = T;
static constexpr S op(S a, S b) { return max(a, b); }
static constexpr S e() { return -infty; }
};
template <class M>
vc<typename M::S> cuml(const vc<typename M::S> &v, int left_index = 0)
{
const int n = v.size();
vc<typename M::S> res(n + 1);
res[0] = M::e();
repi(i, n) res[i + 1] = M::op(res[i], v[i]);
res.erase(res.begin(), res.begin() + left_index);
return res;
}
template <class M>
vc<typename M::S> cumr(const vc<typename M::S> &v, int right_index = 0)
{ return reversed(cuml<M>(reversed(v), right_index)); }
const vpll DRULgrid = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
const vpll DRULplane = {{0, -1}, {1, 0}, {0, 1}, {-1, 0}};
template <class T>
struct is_random_access_iterator
{
static constexpr bool value = is_same_v<
typename iterator_traits<T>::iterator_category,
random_access_iterator_tag
>;
};
template <class T>
constexpr bool is_random_access_iterator_v = is_random_access_iterator<T>::value;
template <class T = ll, class V, class Value, class Comp = ranges::less, class Proj = identity>
inline T LB(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
{ return ranges::lower_bound(v, val, comp, proj) - v.begin(); }
template <class T = ll, class V, class Value, class Comp = ranges::less, class Proj = identity>
inline T UB(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
{ return ranges::upper_bound(v, val, comp, proj) - v.begin(); }
#define DEFAULT_COMP ranges::less
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto lt_cnt(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{ return LB<T>(v, val, comp, proj); }
template <class V, class Value>
inline auto lt_max(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{
auto it = v.lower_bound(val);
return it == v.begin() ? v.end() : prev(it);
}
template <class V, class Value>
inline auto leq_max(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{
auto it = v.upper_bound(val);
return it == v.begin() ? v.end() : prev(it);
}
template <class V, class Value>
inline auto gt_min(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{ return v.upper_bound(val); }
template <class V, class Value>
inline auto geq_min(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{ return v.lower_bound(val); }
template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }
inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); }
inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); }
inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); }
inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); }
inline constexpr ll popcount(ll x) { return std::popcount((ull)x); }
inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); }
#define dump(...)
#define oj(...) __VA_ARGS__
template <class T, class Sequence>
vc<T> content(queue<T, Sequence> que)
{
vc<T> res;
while (!que.empty())
{
res.eb(que.front());
que.pop();
}
return res;
}
template <class T, class Sequence, class Compare>
vc<T> content(priority_queue<T, Sequence, Compare> pque)
{
vc<T> res;
while (!pque.empty())
{
res.eb(pque.top());
pque.pop();
}
return res;
}
template <class T>
auto content(const T &obj) { return obj.content(); }
namespace fastio {
static constexpr uint32_t SIZ = 1 << 17;
char ibuf[SIZ];
char obuf[SIZ];
char out[100];
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SIZ - pir + pil, stdin);
pil = 0;
if (pir < SIZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd1(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd1(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd1_real(T &x) {
string s;
rd1(s);
x = stod(s);
}
template <typename T>
void rd1_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
pil--;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (minus) x = -x;
}
}
void rd1(int &x) { rd1_integer(x); }
void rd1(ll &x) { rd1_integer(x); }
void rd1(i128 &x) { rd1_integer(x); }
void rd1(uint &x) { rd1_integer(x); }
void rd1(ull &x) { rd1_integer(x); }
void rd1(u128 &x) { rd1_integer(x); }
void rd1(double &x) { rd1_real(x); }
void rd1(long double &x) { rd1_real(x); }
template <class T, class U>
void rd1(pair<T, U> &p) {
return rd1(p.first), rd1(p.second);
}
template <size_t N = 0, typename T>
void rd1_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd1(x);
rd1_tuple<N + 1>(t);
}
}
template <class... T>
void rd1(tuple<T...> &tpl) {
rd1_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd1(array<T, N> &x) {
for (auto &d: x) rd1(d);
}
template <class T>
void rd1(vc<T> &x) {
for (auto &d: x) rd1(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd1(h), read(t...);
}
void wt1(const char c) {
if (por == SIZ) flush();
obuf[por++] = c;
}
void wt1(const string s) {
for (char c: s) wt1(c);
}
void wt1(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt1(s[i]);
}
template <typename T>
void wt1_integer(T x) {
if (por > SIZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt1_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt1(s);
}
void wt1(int x) { wt1_integer(x); }
template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void wt1(T x) { wt1_integer(x); }
void wt1(i128 x) { wt1_integer(x); }
void wt1(u128 x) { wt1_integer(x); }
void wt1(double x) { wt1_real(x); }
void wt1(long double x) { wt1_real(x); }
template <class T, class U>
void wt1(const pair<T, U> &val) {
wt1(val.first);
wt1(' ');
wt1(val.second);
}
template <size_t N = 0, typename T>
void wt1_tuple(const T &t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt1(' '); }
const auto x = std::get<N>(t);
wt1(x);
wt1_tuple<N + 1>(t);
}
}
template <class... T>
void wt1(const tuple<T...> &tpl) {
wt1_tuple(tpl);
}
template <class T, size_t S>
void wt1(const array<T, S> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt1(' ');
wt1(val[i]);
}
}
template <class T>
void wt1(const vector<T> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt1(' ');
wt1(val[i]);
}
}
void write() {}
template <class Head, class... Tail>
void write(Head &&head, Tail &&... tail) {
wt1(head);
write(std::forward<Tail>(tail)...);
}
void print() { wt1('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt1(head);
if (sizeof...(Tail)) wt1(' ');
print(std::forward<Tail>(tail)...);
}
}
struct Dummy {
Dummy() { atexit(fastio::flush); }
} dummy;
namespace internal
{
template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }
template <class T>
void READVECnodump(int n, vc<T> &v)
{
v.resize(n);
READnodump(v);
}
template <class T, class... Ts>
void READVECnodump(int n, vc<T> &v, vc<Ts> &...vs)
{ READVECnodump(n, v), READVECnodump(n, vs...); }
template <class T>
void READVEC2nodump(int n, int m, vvc<T> &v)
{
v.assign(n, vc<T>(m));
READnodump(v);
}
template <class T, class... Ts>
void READVEC2nodump(int n, int m, vvc<T> &v, vvc<Ts> &...vs)
{ READVEC2nodump(n, m, v), READVEC2nodump(n, m, vs...); }
template <class T>
void READJAGnodump(int n, vvc<T> &v)
{
v.resize(n);
repi(i, n)
{
int k;
READnodump(k);
READVECnodump(k, v[i]);
}
}
template <class T, class... Ts>
void READJAGnodump(int n, vvc<T> &v, vvc<Ts> &...vs)
{ READJAGnodump(n, v), READJAGnodump(n, vs...); }
};
#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define IN(T,...) T __VA_ARGS__; READ(__VA_ARGS__)
#define LL(...) IN(ll, __VA_ARGS__)
#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define READVEC2(...) internal::READVEC2nodump(__VA_ARGS__); dump(__VA_ARGS__)
#define VEC(T,n,...) vc<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define READJAG(...) internal::READJAGnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define PRINT fastio::print
template <class T, class U, class P>
pair<T, U> operator+=(pair<T, U> &a, const P &b)
{
a.first += b.first;
a.second += b.second;
return a;
}
template <class T, class U, class P>
pair<T, U> operator+(pair<T, U> &a, const P &b) { return a += b; }
template <class T, size_t n, class A>
array<T, n> operator+=(array<T, n> &a, const A &b)
{
for (size_t i = 0; i < n; i++)
a[i] += b[i];
return a;
}
template <class T, size_t n, class A>
array<T, n> operator+(array<T, n> &a, const A &b) { return a += b; }
namespace internal
{
template <size_t... I, class A, class B>
auto tuple_add_impl(A &a, const B &b, const index_sequence<I...>)
{
((get<I>(a) += get<I>(b)), ...);
return a;
}
};
template <class... Ts, class Tp>
tuple<Ts...> operator+=(tuple<Ts...> &a, const Tp &b)
{ return internal::tuple_add_impl(a, b, make_index_sequence<tuple_size_v<tuple<Ts...>>>{}); }
template <class... Ts, class Tp>
tuple<Ts...> operator+(tuple<Ts...> &a, const Tp &b) { return a += b; }
template <class T, class Add>
void offset(vvc<T> &v, const Add &add) { for (auto &vi : v) for (auto &vij : vi) vij += add; }
template <class T, class U>
pair<vc<T>, vc<U>> unzip(const vc<pair<T, U>> &vt)
{
const size_t n = vt.size();
pair<vc<T>, vc<U>> tv;
tv.first.resize(n), tv.second.resize(n);
for (size_t i = 0; i < n; i++)
tie(tv.first[i], tv.second[i]) = vt[i];
return tv;
}
template <class T, class U>
vc<pair<T, U>> zip(const pair<vc<T>, vc<U>> &tv)
{
const size_t n = tv.first.size();
assert(n == tv.second.size());
vc<pair<T, U>> vt(n);
for (size_t i = 0; i < n; i++)
vt[i] = make_pair(tv.first[i], tv.second[i]);
return vt;
}
namespace internal
{
template <size_t... I, class V, class Tp>
auto vt_to_tv_impl(V &tv, const Tp &t, index_sequence<I...>, size_t index)
{ ((get<I>(tv)[index] = get<I>(t)), ...); }
template <size_t... I, class Tp>
auto tv_to_vt_impl(const Tp &tv, index_sequence<I...>, size_t index)
{ return make_tuple(get<I>(tv)[index]...); }
};
template <class... Ts>
auto unzip(const vc<tuple<Ts...>> &vt)
{
const size_t n = vt.size();
tuple<vc<Ts>...> tv;
apply([&](auto &...v)
{ ((v.resize(n)), ...); }, tv);
for (size_t i = 0; i < n; i++)
internal::vt_to_tv_impl(tv, vt[i], make_index_sequence<tuple_size_v<decltype(tv)>>{}, i);
return tv;
}
template <class... Ts>
auto zip(const tuple<vc<Ts>...> &tv)
{
size_t n = get<0>(tv).size();
apply([&](auto &...v)
{ ((assert(v.size() == n)), ...); }, tv);
vc<tuple<Ts...>> vt(n);
for (size_t i = 0; i < n; i++)
vt[i] = internal::tv_to_vt_impl(tv, index_sequence_for<Ts...>{}, i);
return vt;
}
mt19937_64 mt;
template <class T = ll, class U1, class U2>
T randint(U1 l, U2 r)
{
assert(T(l) <= T(r));
return T(l) + mt() % (T(r) - T(l) + 1);
}
template <class T>
struct larger_int
{
using type = T;
};
#define LARGER_INT(T,U) template <> struct larger_int<T> { using type = U; };
LARGER_INT(signed char, short)
LARGER_INT(short, int)
LARGER_INT(int, long long)
LARGER_INT(long, __int128_t)
LARGER_INT(long long, __int128_t)
LARGER_INT(unsigned char, unsigned short)
LARGER_INT(unsigned short, unsigned int)
LARGER_INT(unsigned int, unsigned long long)
LARGER_INT(unsigned long, __uint128_t)
LARGER_INT(unsigned long long, __uint128_t)
#undef LARGER_INT
template <class T>
using larger_int_t = typename larger_int<T>::type;
namespace internal
{
template <class T>
constexpr ll powmod_constexpr(ll x, ll n, T m)
{
if (m == 1)
return 0;
using U = make_unsigned_t<T>;
using L = larger_int_t<U>;
U r = 1, y = safemod(x, m);
while (n)
{
if (n & 1)
r = L(r) * y % m;
y = L(y) * y % m;
n >>= 1;
}
return r;
}
template <class T>
constexpr bool isprime_constexpr(T n)
{
if constexpr (sizeof(T) > 4)
{
if (n <= INT_MAX)
return isprime_constexpr<int>(n);
}
if (n <= 1)
return false;
if (n == 2 || n == 7 || n == 61)
return true;
if (n % 2 == 0)
return false;
ll d = n - 1;
while (d % 2 == 0)
d /= 2;
using U = make_unsigned_t<T>;
using L = larger_int_t<U>;
auto miller_rabin = [&](const auto &bases) constexpr
{
for (ll a : bases)
{
ll t = d, y = powmod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1)
{
y = L(y) * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0)
return false;
}
return true;
};
if constexpr(sizeof(T) <= 4)
{
constexpr ll bases[3] = {2, 7, 61};
return miller_rabin(bases);
}
else
{
constexpr ll bases[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
return miller_rabin(bases);
}
}
template <auto n>
constexpr bool isprime = isprime_constexpr(n);
};
namespace internal
{
template <auto M>
struct policy_static
{
using mod_type = decltype(M);
using value_type = make_unsigned_t<mod_type>;
using calc_type = larger_int_t<value_type>;
static constexpr bool is_prime = isprime_constexpr(M);
static constexpr mod_type mod() { return M; }
static constexpr value_type umod() { return M; }
static constexpr value_type init(value_type v) { return v; }
static constexpr mod_type val(value_type v) { return v; }
static constexpr value_type mul(value_type a, value_type b)
{
return (value_type)((calc_type(a) * b) % M);
}
};
};
namespace internal
{
struct barrett32
{
uint m;
ull im;
explicit barrett32(uint m) : m(m), im((ull)(-1) / m + 1) {}
uint umod() const { return m; }
uint mul(uint a, uint b) const
{
ull z = a;
z *= b;
ull x = ull((u128(z) * im) >> 64);
ull y = x * m;
return uint(z - y + (z < y ? m : 0));
}
};
template <int id>
struct policy_barrett32
{
using value_type = uint;
using calc_type = ull;
using mod_type = int;
static constexpr bool is_prime = false;
static inline barrett32 reducer{998244353};
static void set_mod(mod_type m) { reducer = barrett32(m); }
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return v; }
static mod_type val(value_type v) { return v; }
static value_type mul(value_type a, value_type b) { return reducer.mul(a, b); }
};
};
namespace internal
{
inline constexpr ull inv64(ull a)
{
ull x = a;
while (a * x != 1) x *= 2 - a * x;
return x;
}
struct montgomery64odd
{
ull m, im, sq;
explicit montgomery64odd(ull m) : m(m), im(inv64(m)), sq(-u128(m) % m) {}
ull umod() const { return m; }
ull reduce(u128 x) const
{
auto t = (x + u128(m) * (-im * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * sq); }
};
struct montgomery64
{
ull m, mx, imx, d, q;
uint b;
explicit montgomery64(ull m) : m(m)
{
b = countr_zero(m), mx = m >> b;
imx = inv64(mx);
d = powmod_constexpr((mx + 1) / 2, b, mx);
u128 sq = -u128(mx) % mx;
q = (1 + (((sq - 1) * d) << b)) % m;
}
ull umod() const { return m; }
ull reduce(u128 x) const
{
ull p = x & MASK(b);
x = (x >> b) + p * d;
ull y = p << (64 - b);
auto t = (x + u128(mx) * (imx * (y - ull(x)))) >> (64 - b);
if (t >= m) { t -= m; if (t >= m) t -= m; }
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * q); }
};
template <int id>
struct policy_montgomery64_odd
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64odd reducer{(1LL << 61) - 1};
static void set_mod(mod_type m) { reducer = montgomery64odd(m); }
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v) { return reducer.reduce(v); }
static value_type mul(value_type a, value_type b) { return reducer.reduce((calc_type)a * b); }
};
template <int id>
struct policy_montgomery64
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64 reducer{(1LL << 61) - 1};
static void set_mod(mod_type m) { reducer = montgomery64(m); }
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v) { return reducer.reduce(v); }
static value_type mul(value_type a, value_type b) { return reducer.reduce((calc_type)a * b); }
};
};
template <class T = ll>
constexpr tuple<T, T, T> extgcd(T a, T b)
{
if (a == 0 && b == 0)
return {0, 0, 0};
T x1 = 1, y1 = 0, z1 = a;
T x2 = 0, y2 = 1, z2 = b;
while (z2 != 0)
{
T q = z1 / z2;
tie(x1, x2) = make_pair(x2, x1 - q * x2);
tie(y1, y2) = make_pair(y2, y1 - q * y2);
tie(z1, z2) = make_pair(z2, z1 - q * z2);
}
if (z1 < 0)
x1 = -x1, y1 = -y1, z1 = -z1;
return {z1, x1, y1};
}
namespace internal
{
template <class Policy>
struct modint_impl
{
using V = typename Policy::value_type;
using M = typename Policy::mod_type;
using mint = modint_impl;
private:
V _v;
public:
static constexpr M mod() { return Policy::mod(); }
template <class T = Policy>
static auto set_mod(M m) -> decltype(T::set_mod(m)) { return T::set_mod(m); }
static mint raw(V v)
{
mint x;
x._v = v;
return x;
}
modint_impl() : _v(0) {}
template <class T, typename = enable_if_t<is_integral_ext<T>>>
modint_impl(T v)
{
V rem;
if constexpr (is_signed_ext<T>)
{
using S = make_signed_t<V>;
S x = v % S(Policy::umod());
if (x < 0)
x += Policy::umod();
rem = x;
}
else
rem = V(v % Policy::umod());
_v = Policy::init(rem);
};
M val() const { return Policy::val(_v); }
mint &operator+=(const mint &rhs)
{
_v += rhs._v;
if (_v >= Policy::umod())
_v -= Policy::umod();
return *this;
}
mint &operator-=(const mint &rhs)
{
_v -= rhs._v;
if (_v >= Policy::umod())
_v += Policy::umod();
return *this;
}
mint &operator*=(const mint &rhs)
{
_v = Policy::mul(_v, rhs._v);
return *this;
}
mint &operator/=(const mint &rhs)
{
return *this *= rhs.inv();
}
mint &operator++()
{
_v++;
if (_v == Policy::umod())
_v = 0;
return *this;
}
mint &operator--()
{
if (_v == 0)
_v = Policy::umod();
_v--;
return *this;
}
mint operator++(int)
{
mint res = *this;
++(*this);
return res;
}
mint operator--(int)
{
mint res = *this;
--(*this);
return res;
}
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
template <class T>
mint pow(T n) const
{
assert(n >= 0);
mint x = *this, r = 1;
while (n)
{
if (n & 1)
r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const
{
if constexpr (Policy::is_prime)
{
return pow(mod() - 2);
}
else
{
auto [g, x, y] = extgcd<M>(val(), mod());
assert(g == 1);
return mint(x);
}
}
friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
friend void rd1(mint &x)
{
long long a;
fastio::rd1(a);
x = a;
}
friend void wt1(const mint &x)
{
fastio::wt1(x.val());
}
};
};
template <int mod>
using static_modint32 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint32 = internal::modint_impl<internal::policy_barrett32<id>>;
template <ll mod>
using static_modint64 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint64_odd = internal::modint_impl<internal::policy_montgomery64_odd<id>>;
template <int id>
using dynamic_modint64 = internal::modint_impl<internal::policy_montgomery64<id>>;
using modint998244353 = static_modint32<998244353>;
template <class T>
struct is_modint : std::false_type
{
};
template <class Policy>
struct is_modint<internal::modint_impl<Policy>> : std::true_type
{
};
template <class T>
inline constexpr bool is_modint_v = is_modint<T>::value;
template <class T>
struct is_static_modint : false_type {};
template <int m>
struct is_static_modint<static_modint32<m>> : true_type {};
template <ll m>
struct is_static_modint<static_modint64<m>> : true_type {};
template <class T>
inline constexpr bool is_static_modint_v = is_static_modint<T>::value;
template <class T>
struct is_dynamic_modint : false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint32<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64_odd<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64<id>> : true_type {};
template <class T>
inline constexpr bool is_dynamic_modint_v = is_dynamic_modint<T>::value;
template <typename, typename = void>
struct has_mod : std::false_type
{
};
template <typename T>
struct has_mod<T, std::void_t<decltype(T::mod())>> : std::true_type
{
};
template <class mint>
struct PowerTable
{
private:
decltype(mint::mod()) mod;
mint base;
vc<mint> pw;
public:
PowerTable() {}
PowerTable(const mint &base) : mod(mint::mod()), base(base), pw(1, 1) {}
void reserve(int n)
{
if (mod != mint::mod())
{
mod = mint::mod();
pw = {1};
}
int i = pw.size();
if (n < i)
return;
pw.resize(n + 1);
for (; i <= n; i++)
pw[i] = pw[i - 1] * base;
}
mint pow(int n)
{
reserve(n);
return pw[n];
}
};
template <class T>
struct Binomial
{
private:
inline static decltype(T::mod()) mod;
public:
inline static vc<T> fac_, finv_, inv_;
static void reserve(int n)
{
if constexpr (is_dynamic_modint_v<T>)
{
if (mod != T::mod())
{
mod = T::mod();
fac_ = {1, 1}, finv_ = {1, 1}, inv_ = {0, 1};
}
}
else
{
if (fac_.empty())
fac_ = {1, 1}, finv_ = {1, 1}, inv_ = {0, 1};
}
if (n < SZ(fac_))
return;
chmin(n, T::mod() - 1);
int si = fac_.size();
fac_.resize(n + 1), finv_.resize(n + 1), inv_.resize(n + 1);
repi(i, si, n + 1)
{
fac_[i] = fac_[i - 1] * T::raw(i);
inv_[i] = -inv_[T::mod() % i] * T::raw(T::mod() / i);
finv_[i] = finv_[i - 1] * inv_[i];
}
}
static T inv(int n)
{
assert(n != 0);
reserve(n);
return inv_[n];
}
static T C(int n, int k)
{
if (n < k)
return 0;
if (n < 0 || k < 0)
return 0;
reserve(n);
return fac_[n] * finv_[k] * finv_[n - k];
}
};
template <class T = ll, class U = larger_int_t<T>>
pair<T, T> svp2d(const pair<T, T> &a, const pair<T, T> &b)
{
assert((a != pair<T, T>{0, 0} && b != pair<T, T>{0, 0}));
auto [a1, a2] = a;
auto [b1, b2] = b;
if ((U)a1 * a1 + (U)a2 * a2 < (U)b1 * b1 + (U)b2 * b2)
swap(a1, b1), swap(a2, b2);
while ((U)a1 * a1 + (U)a2 * a2 > (U)b1 * b1 + (U)b2 * b2)
{
swap(a1, b1), swap(a2, b2);
T k = divround<U>((U)a1 * b1 + (U)a2 * b2, (U)a1 * a1 + (U)a2 * a2);
b1 -= k * a1, b2 -= k * a2;
}
return {a1, a2};
}
template <class mint>
pair<decltype(mint(0).val()), decltype(mint(0).val())>
mint_to_rat(const mint &x)
{
auto [p, q] = svp2d({x.val(), 1}, {mint::mod(), 0});
if (q < 0)
p = -p, q = -q;
return {p, q};
}
namespace cpp_dump
{
struct mint_to_rat_fn
{
template <class T>
constexpr auto operator()(const T &x) const -> decltype(mint_to_rat(x))
{
return mint_to_rat(x);
}
};
struct rat_closure : std::ranges::range_adaptor_closure<rat_closure>
{
template <typename T>
constexpr auto operator()(T &&t) const
{
if constexpr (!std::ranges::range<T> && std::invocable<mint_to_rat_fn, decltype(std::forward<T>(t))>)
{
return mint_to_rat_fn{}(std::forward<T>(t));
}
else if constexpr (std::ranges::range<T>)
{
using Ref = std::ranges::range_reference_t<T>;
if constexpr (std::invocable<mint_to_rat_fn, decltype(std::forward<Ref>(std::declval<Ref>()))>)
{
return std::forward<T>(t) | std::views::transform(mint_to_rat_fn{});
}
else if constexpr (std::ranges::range<Ref>)
{
return std::forward<T>(t) | std::views::transform([this](auto &&inner)
{ return (*this)(std::forward<decltype(inner)>(inner)); });
}
else
{
static_assert(false);
}
}
else
{
static_assert(false);
}
}
};
template <typename T>
requires(!std::ranges::range<T> && std::invocable<mint_to_rat_fn, T>)
constexpr auto operator|(T &&t, const rat_closure &c)
{
return c(std::forward<T>(t));
}
}
using mint = modint998244353;
using bi = Binomial<mint>;
void init()
{
oj(mt.seed(random_device()()));
}
struct use_std_nth_element {
template <class RandomIt, class Compare>
void operator()(RandomIt first, RandomIt nth, RandomIt last,
Compare comp) const {
std::nth_element(first, nth, last, comp);
}
};
struct use_median_of_medians {
private:
template <class RandomIt, class Compare>
static void select_impl(RandomIt first, RandomIt nth, RandomIt last,
Compare comp) {
using difference_type =
typename std::iterator_traits<RandomIt>::difference_type;
using value_type =
typename std::iterator_traits<RandomIt>::value_type;
constexpr difference_type small_limit = 32;
while (last - first > small_limit) {
RandomIt medians_end = first;
for (RandomIt group_first = first; group_first < last;
group_first += 5) {
const difference_type remaining = last - group_first;
RandomIt group_last =
group_first + std::min<difference_type>(5, remaining);
std::sort(group_first, group_last, comp);
RandomIt median = group_first + (group_last - group_first) / 2;
std::iter_swap(medians_end, median);
++medians_end;
}
RandomIt pivot_pos = first + (medians_end - first) / 2;
select_impl(first, pivot_pos, medians_end, comp);
const value_type pivot = *pivot_pos;
RandomIt equal_first = std::partition(
first, last,
[&](const value_type& x) { return comp(x, pivot); });
RandomIt equal_last = std::partition(
equal_first, last,
[&](const value_type& x) { return !comp(pivot, x); });
if (nth < equal_first) {
last = equal_first;
} else if (nth >= equal_last) {
first = equal_last;
} else {
return;
}
}
std::sort(first, last, comp);
}
public:
template <class RandomIt, class Compare>
void operator()(RandomIt first, RandomIt nth, RandomIt last,
Compare comp) const {
assert(first <= nth && nth < last);
select_impl(first, nth, last, comp);
}
};
namespace sorted_matrix_selection_detail {
using rank_type = std::uint64_t;
enum class answer_kind : unsigned char { upper, lower, middle };
struct answer_location {
answer_kind kind;
rank_type middle_rank = 0;
};
template <class Accessor, class Compare, class LocalSelector>
class selector {
public:
using value_type = std::decay_t<
std::invoke_result_t<Accessor&, std::size_t, std::size_t>>;
selector(std::size_t n, Accessor accessor, Compare compare,
LocalSelector local_selector)
: original_n_(n),
accessor_(std::move(accessor)),
compare_(std::move(compare)),
local_selector_(std::move(local_selector)) {}
value_type run(rank_type k) {
if (original_n_ == 0) {
throw std::invalid_argument(
"sorted_matrix_select: n must be positive");
}
const rank_type rank_n = static_cast<rank_type>(original_n_);
if (static_cast<std::size_t>(rank_n) != original_n_ ||
rank_n > std::numeric_limits<rank_type>::max() / rank_n) {
throw std::overflow_error(
"sorted_matrix_select: n*n does not fit in uint64_t");
}
const rank_type total = rank_n * rank_n;
if (k >= total) {
throw std::out_of_range(
"sorted_matrix_select: k is outside [0, n*n)");
}
std::vector<std::size_t> positions(original_n_);
std::iota(positions.begin(), positions.end(), std::size_t{0});
return biselect(positions, k + 1, k + 1).first;
}
private:
value_type at(const std::vector<std::size_t>& positions,
std::size_t i, std::size_t j) {
return std::invoke(accessor_, positions[i],
original_n_ - 1 - positions[j]);
}
bool less(const value_type& x, const value_type& y) {
return std::invoke(compare_, x, y);
}
static rank_type ceil_div4(rank_type x) {
return x / 4 + static_cast<rank_type>(x % 4 != 0);
}
static rank_type ceil_div4_sum(rank_type x, rank_type y) {
return x / 4 + y / 4 +
static_cast<rank_type>((x % 4 + y % 4 + 3) / 4);
}
std::pair<value_type, value_type>
biselect(const std::vector<std::size_t>& positions,
rank_type k1, rank_type k2) {
const std::size_t n = positions.size();
const rank_type total = static_cast<rank_type>(n) * n;
assert(n > 0);
assert(1 <= k2 && k2 <= k1 && k1 <= total);
if (n <= 2) {
std::vector<value_type> values;
values.reserve(n * n);
for (std::size_t i = 0; i < n; ++i) {
for (std::size_t j = 0; j < n; ++j) {
values.push_back(at(positions, i, j));
}
}
std::sort(values.begin(), values.end(), std::ref(compare_));
return {values[static_cast<std::size_t>(k1 - 1)],
values[static_cast<std::size_t>(k2 - 1)]};
}
const std::size_t sub_n = (n + 2) / 2;
std::vector<std::size_t> sub_positions(sub_n);
for (std::size_t i = 0; i < sub_n; ++i) {
sub_positions[i] = positions[std::min(2 * i, n - 1)];
}
rank_type sub_k1;
if ((n & 1U) == 0) {
sub_k1 = static_cast<rank_type>(n) + 1 + ceil_div4(k1);
} else {
sub_k1 = ceil_div4_sum(
k1, 2 * static_cast<rank_type>(n) + 1);
}
const rank_type sub_k2 = ceil_div4(k2);
const rank_type sub_total =
static_cast<rank_type>(sub_n) * sub_n;
assert(1 <= sub_k2 && sub_k2 <= sub_k1 &&
sub_k1 <= sub_total);
auto [upper, lower] =
biselect(sub_positions, sub_k1, sub_k2);
assert(!less(upper, lower));
rank_type rank_less_upper = 0;
rank_type rank_greater_lower = 0;
std::size_t first_less_upper = 0;
std::size_t first_not_greater_lower = 0;
for (std::size_t i = 0; i < n; ++i) {
while (first_less_upper < n) {
value_type x = at(positions, i, first_less_upper);
if (less(x, upper)) break;
++first_less_upper;
}
rank_less_upper += n - first_less_upper;
while (first_not_greater_lower < n) {
value_type x =
at(positions, i, first_not_greater_lower);
if (!less(lower, x)) break;
++first_not_greater_lower;
}
rank_greater_lower += first_not_greater_lower;
}
const auto locate = [&](rank_type k) -> answer_location {
if (rank_less_upper <= k - 1) {
return {answer_kind::upper, 0};
}
const rank_type count_not_greater_lower =
total - rank_greater_lower;
if (k <= count_not_greater_lower) {
return {answer_kind::lower, 0};
}
return {answer_kind::middle,
k - count_not_greater_lower};
};
const answer_location where1 = locate(k1);
const answer_location where2 = locate(k2);
if (where1.kind != answer_kind::middle &&
where2.kind != answer_kind::middle) {
return {where1.kind == answer_kind::upper ? upper : lower,
where2.kind == answer_kind::upper ? upper : lower};
}
assert(less(lower, upper));
assert(rank_less_upper + rank_greater_lower >= total);
const rank_type middle_count =
rank_less_upper - (total - rank_greater_lower);
assert(middle_count <=
static_cast<rank_type>(
std::numeric_limits<std::size_t>::max()));
std::vector<value_type> middle;
middle.reserve(static_cast<std::size_t>(middle_count));
first_less_upper = 0;
first_not_greater_lower = 0;
for (std::size_t i = 0; i < n; ++i) {
while (first_less_upper < n) {
value_type x = at(positions, i, first_less_upper);
if (less(x, upper)) break;
++first_less_upper;
}
while (first_not_greater_lower < n) {
value_type x =
at(positions, i, first_not_greater_lower);
if (!less(lower, x)) break;
++first_not_greater_lower;
}
for (std::size_t j = first_less_upper;
j < first_not_greater_lower; ++j) {
middle.push_back(at(positions, i, j));
}
}
assert(middle.size() == middle_count);
const auto pick = [&](rank_type r) -> value_type {
assert(1 <= r && r <= middle.size());
auto nth = middle.begin() + static_cast<std::ptrdiff_t>(r - 1);
std::invoke(local_selector_, middle.begin(), nth, middle.end(),
std::ref(compare_));
return *nth;
};
value_type answer1 =
where1.kind == answer_kind::upper
? upper
: where1.kind == answer_kind::lower
? lower
: pick(where1.middle_rank);
value_type answer2 =
where2.kind == answer_kind::upper
? upper
: where2.kind == answer_kind::lower
? lower
: pick(where2.middle_rank);
return {std::move(answer1), std::move(answer2)};
}
std::size_t original_n_;
Accessor accessor_;
Compare compare_;
LocalSelector local_selector_;
};
}
template <class Accessor, class Compare = std::less<>>
auto sorted_matrix_select(std::size_t n, std::uint64_t k,
Accessor accessor, Compare compare = {}) {
using impl = sorted_matrix_selection_detail::selector<
Accessor, Compare, use_std_nth_element>;
return impl(n, std::move(accessor), std::move(compare),
use_std_nth_element{})
.run(k);
}
template <class T>
inline constexpr bool is_rational_ordered_v = is_integral_ext<T> || is_floating_point_v<T>;
template <class T>
struct Rational
{
using value_type = T;
T num, den;
private:
void normalize_sign()
{
if constexpr (is_signed_ext<T> || is_floating_point_v<T>)
if (den < T(0))
num = -num, den = -den;
}
static T gcd_abs(T a, T b)
{
if constexpr (is_signed_ext<T>)
{
if (a < 0) a = -a;
if (b < 0) b = -b;
}
while (b != T(0))
{
T r = a % b;
a = b, b = r;
}
return a;
}
public:
Rational() : num(0), den(1) {}
Rational(const T &num) : num(num), den(1) {}
Rational(const T &num, const T &den) : num(num), den(den)
{
assert(den != T(0));
normalize_sign();
}
pair<T, T> reduced() const
{
if constexpr (is_integral_ext<T>)
{
T g = gcd_abs(num, den);
return g == T(0) ? pair<T, T>{num, den} : pair<T, T>{num / g, den / g};
}
else
return {num, den};
}
Rational operator-() const { return {-num, den}; }
Rational operator+() const { return *this; }
Rational &operator+=(const Rational &rhs)
{
T rhs_num = rhs.num, rhs_den = rhs.den;
num = num * rhs_den + rhs_num * den;
den *= rhs_den;
normalize_sign();
return *this;
}
Rational &operator-=(const Rational &rhs)
{
T rhs_num = rhs.num, rhs_den = rhs.den;
num = num * rhs_den - rhs_num * den;
den *= rhs_den;
normalize_sign();
return *this;
}
Rational &operator*=(const Rational &rhs)
{
T rhs_num = rhs.num, rhs_den = rhs.den;
num *= rhs_num;
den *= rhs_den;
normalize_sign();
return *this;
}
Rational &operator/=(const Rational &rhs)
{
assert(rhs.num != T(0));
T rhs_num = rhs.num, rhs_den = rhs.den;
num *= rhs_den;
den *= rhs_num;
normalize_sign();
return *this;
}
friend Rational operator+(Rational lhs, const Rational &rhs) { return lhs += rhs; }
friend Rational operator-(Rational lhs, const Rational &rhs) { return lhs -= rhs; }
friend Rational operator*(Rational lhs, const Rational &rhs) { return lhs *= rhs; }
friend Rational operator/(Rational lhs, const Rational &rhs) { return lhs /= rhs; }
friend bool operator==(const Rational &lhs, const Rational &rhs)
{
using C = larger_int_t<T>;
return C(lhs.num) * C(rhs.den) == C(rhs.num) * C(lhs.den);
}
friend bool operator!=(const Rational &lhs, const Rational &rhs) { return !(lhs == rhs); }
template <class U = T, enable_if_t<is_rational_ordered_v<U>, int> = 0>
friend bool operator<(const Rational &lhs, const Rational &rhs)
{
using C = larger_int_t<T>;
return C(lhs.num) * C(rhs.den) < C(rhs.num) * C(lhs.den);
}
template <class U = T, enable_if_t<is_rational_ordered_v<U>, int> = 0>
friend bool operator>(const Rational &lhs, const Rational &rhs) { return rhs < lhs; }
template <class U = T, enable_if_t<is_rational_ordered_v<U>, int> = 0>
friend bool operator<=(const Rational &lhs, const Rational &rhs) { return !(rhs < lhs); }
template <class U = T, enable_if_t<is_rational_ordered_v<U>, int> = 0>
friend bool operator>=(const Rational &lhs, const Rational &rhs) { return !(lhs < rhs); }
friend ostream &operator<<(ostream &os, const Rational &x)
{
auto [num, den] = x.reduced();
return os << num << '/' << den;
}
friend void wt1(const Rational &x)
{
auto [num, den] = x.reduced();
using fastio::wt1;
wt1(num), wt1('/'), wt1(den);
}
};
template <class T>
struct is_rational : false_type
{};
template <class T>
struct is_rational<Rational<T>> : true_type
{};
template <class T>
inline constexpr bool is_rational_v = is_rational<T>::value;
namespace std
{
template <class T>
struct numeric_limits<::Rational<T>> : numeric_limits<T>
{
static constexpr bool is_specialized = numeric_limits<T>::is_specialized;
static ::Rational<T> min() noexcept { return ::Rational<T>(numeric_limits<T>::min()); }
static ::Rational<T> lowest() noexcept { return ::Rational<T>(numeric_limits<T>::lowest()); }
static ::Rational<T> max() noexcept { return ::Rational<T>(numeric_limits<T>::max()); }
static constexpr bool is_signed = numeric_limits<T>::is_signed;
static constexpr bool is_integer = false;
static constexpr bool is_exact = numeric_limits<T>::is_exact;
};
}
void main2()
{
LL(N);
VEC(ll, N, A);
sort(ALL(A));
auto ans = sorted_matrix_select(N, N * (N - 1) / 2, [&](ll i, ll j)
{ return Rational<int>(A[i], A[j]); });
PRINT(ans.reduced());
}
void test()
{
}
template <auto init, auto main2, auto test>
struct Main
{
Main()
{
cauto CERR = [](string val, string color)
{
string s = "\033[" + color + "m" + val + "\033[m";
};
CERR("\n[FAST_IO]\n\n", "32");
cout << fixed << setprecision(20);
init();
CERR("\n[SINGLE_TESTCASE]\n\n", "36");
main2();
}
};
Main<init, main2, test> main_dummy;
int main() {}