結果
| 問題 | No.2262 Fractions |
| ユーザー |
 noimi
|
| 提出日時 | 2024-11-13 01:03:33 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 41,352 bytes |
| コンパイル時間 | 5,572 ms |
| コンパイル使用メモリ | 388,568 KB |
| 実行使用メモリ | 10,880 KB |
| 最終ジャッジ日時 | 2024-11-13 01:04:18 |
| 合計ジャッジ時間 | 28,486 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 1,667 ms
10,880 KB |
| testcase_01 | AC | 291 ms
5,632 KB |
| testcase_02 | AC | 320 ms
5,632 KB |
| testcase_03 | AC | 363 ms
5,632 KB |
| testcase_04 | AC | 366 ms
5,632 KB |
| testcase_05 | AC | 355 ms
5,504 KB |
| testcase_06 | AC | 398 ms
5,632 KB |
| testcase_07 | AC | 369 ms
5,632 KB |
| testcase_08 | AC | 374 ms
5,760 KB |
| testcase_09 | AC | 403 ms
5,504 KB |
| testcase_10 | AC | 386 ms
5,632 KB |
| testcase_11 | AC | 1,648 ms
5,632 KB |
| testcase_12 | AC | 1,662 ms
5,504 KB |
| testcase_13 | AC | 1,675 ms
5,632 KB |
| testcase_14 | AC | 1,708 ms
5,632 KB |
| testcase_15 | AC | 1,667 ms
5,632 KB |
| testcase_16 | AC | 934 ms
5,504 KB |
| testcase_17 | AC | 911 ms
5,504 KB |
| testcase_18 | AC | 931 ms
5,632 KB |
| testcase_19 | TLE | - |
| testcase_20 | TLE | - |
| testcase_21 | TLE | - |
| testcase_22 | TLE | - |
| testcase_23 | TLE | - |
| testcase_24 | TLE | - |
| testcase_25 | TLE | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
| testcase_42 | -- | - |
| testcase_43 | -- | - |
| testcase_44 | -- | - |
| testcase_45 | -- | - |
ソースコード
#pragma region Macros
#ifdef noimi
#pragma comment(linker, "/stack:256000000")
#include "my_template.hpp"
#else
// #pragma GCC target("avx2")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#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 <immintrin.h>
#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 <utility>
#include <variant>
#ifdef noimi
#define oj_local(a, b) b
#else
#define oj_local(a, b) a
#endif
#define LOCAL if(oj_local(0, 1))
#define OJ if(oj_local(1, 0))
using namespace std;
using ll = long long;
using ull = unsigned long long int;
using i128 = __int128_t;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using ld = long double;
template <typename T> using vc = vector<T>;
template <typename T> using vvc = vector<vc<T>>;
template <typename T> using vvvc = vector<vvc<T>>;
using vi = vc<int>;
using vl = vc<ll>;
using vpi = vc<pii>;
using vpl = vc<pll>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
template <typename T> int si(const T &x) { return x.size(); }
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); }
vi iota(int n) {
vi a(n);
return iota(a.begin(), a.end(), 0), a;
}
template <typename T> vi iota(const vector<T> &a, bool greater = false) {
vi res(a.size());
iota(res.begin(), res.end(), 0);
sort(res.begin(), res.end(), [&](int i, int j) {
if(greater) return a[i] > a[j];
return a[i] < a[j];
});
return res;
}
// macros
#define overload5(a, b, c, d, e, name, ...) name
#define overload4(a, b, c, d, name, ...) name
#define endl '\n'
#define REP0(n) for(ll jidlsjf = 0; jidlsjf < n; ++jidlsjf)
#define REP1(i, n) for(ll i = 0; i < (n); ++i)
#define REP2(i, a, b) for(ll i = (a); i < (b); ++i)
#define REP3(i, a, b, c) for(ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__)
#define per0(n) for(int jidlsjf = 0; jidlsjf < (n); ++jidlsjf)
#define per1(i, n) for(ll i = (n) - 1; i >= 0; --i)
#define per2(i, a, b) for(ll i = (a) - 1; i >= b; --i)
#define per3(i, a, b, c) for(ll i = (a) - 1; i >= (b); i -= (c))
#define per(...) overload4(__VA_ARGS__, per3, per2, per1, per0)(__VA_ARGS__)
#define fore0(a) rep(a.size())
#define fore1(i, a) for(auto &&i : a)
#define fore2(a, b, v) for(auto &&[a, b] : v)
#define fore3(a, b, c, v) for(auto &&[a, b, c] : v)
#define fore4(a, b, c, d, v) for(auto &&[a, b, c, d] : v)
#define fore(...) overload5(__VA_ARGS__, fore4, fore3, fore2, fore1, fore0)(__VA_ARGS__)
#define setbits(j, n) for(ll iiiii = (n), j = lowbit(iiiii); iiiii; iiiii ^= 1 << j, j = lowbit(iiiii))
#define perm(v) for(bool permrepflag = true; (permrepflag ? exchange(permrepflag, false) : next_permutation(all(v)));)
#define fi first
#define se second
#define pb push_back
#define ppb pop_back
#define ppf pop_front
#define eb emplace_back
#define drop(s) cout << #s << endl, exit(0)
#define si(c) (int)(c).size()
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define lbg(c, x) distance((c).begin(), lower_bound(all(c), (x), greater{}))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define ubg(c, x) distance((c).begin(), upper_bound(all(c), (x), greater{}))
#define rng(v, l, r) v.begin() + (l), v.begin() + (r)
#define all(c) begin(c), end(c)
#define rall(c) rbegin(c), rend(c)
#define SORT(v) sort(all(v))
#define REV(v) reverse(all(v))
#define UNIQUE(x) SORT(x), x.erase(unique(all(x)), x.end())
template <typename T = ll, typename S> T SUM(const S &v) { return accumulate(all(v), T(0)); }
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define overload2(_1, _2, name, ...) name
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#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__))))
constexpr pii dx4[4] = {pii{1, 0}, pii{0, 1}, pii{-1, 0}, pii{0, -1}};
constexpr pii dx8[8] = {{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};
namespace yesno_impl {
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
const string yesno[2] = {"no", "yes"};
const string firstsecond[2] = {"second", "first"};
const string FirstSecond[2] = {"Second", "First"};
const string possiblestr[2] = {"impossible", "possible"};
const string Possiblestr[2] = {"Impossible", "Possible"};
void YES(bool t = 1) { cout << YESNO[t] << endl; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { cout << YesNo[t] << endl; }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { cout << yesno[t] << endl; }
void no(bool t = 1) { yes(!t); }
void first(bool t = 1) { cout << firstsecond[t] << endl; }
void First(bool t = 1) { cout << FirstSecond[t] << endl; }
void possible(bool t = 1) { cout << possiblestr[t] << endl; }
void Possible(bool t = 1) { cout << Possiblestr[t] << endl; }
}; // namespace yesno_impl
using namespace yesno_impl;
#define INT(...) \
int __VA_ARGS__; \
IN(__VA_ARGS__)
#define INTd(...) \
int __VA_ARGS__; \
IN2(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
IN(__VA_ARGS__)
#define LLd(...) \
ll __VA_ARGS__; \
IN2(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
IN(__VA_ARGS__)
#define CHR(...) \
char __VA_ARGS__; \
IN(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
IN(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
IN(name)
#define VECd(type, name, size) \
vector<type> name(size); \
IN2(name)
#define VEC2(type, name1, name2, size) \
vector<type> name1(size), name2(size); \
for(int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC2d(type, name1, name2, size) \
vector<type> name1(size), name2(size); \
for(int i = 0; i < size; i++) IN2(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size) \
vector<type> name1(size), name2(size), name3(size); \
for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC3d(type, name1, name2, name3, size) \
vector<type> name1(size), name2(size), name3(size); \
for(int i = 0; i < size; i++) IN2(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size) \
vector<type> name1(size), name2(size), name3(size), name4(size); \
for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VEC4d(type, name1, name2, name3, name4, size) \
vector<type> name1(size), name2(size), name3(size), name4(size); \
for(int i = 0; i < size; i++) IN2(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
IN(name)
#define VVd(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
IN2(name)
int scan() { return getchar(); }
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T, class S> void scan(pair<T, S> &p) { scan(p.first), scan(p.second); }
template <class T> void scan(vector<T> &);
template <class T> void scan(vector<T> &a) {
for(auto &i : a) scan(i);
}
template <class T> void scan(T &a) { cin >> a; }
void IN() {}
void IN2() {}
template <class Head, class... Tail> void IN(Head &head, Tail &...tail) {
scan(head);
IN(tail...);
}
template <class Head, class... Tail> void IN2(Head &head, Tail &...tail) {
scan(head);
--head;
IN2(tail...);
}
template <int p = -1> void pat() {}
template <int p = -1, class Head, class... Tail> void pat(Head &h, Tail &...tail) {
h += p;
pat<p>(tail...);
}
template <typename T, typename S> T ceil(T x, S y) {
assert(y);
return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y));
}
template <typename T, typename S> T floor(T x, S y) {
assert(y);
return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1)));
}
template <typename T, typename S, typename U> U bigmul(const T &x, const S &y, const U &lim) { // clamp(x * y, -lim, lim)
if(x < 0 and y < 0) return bigmul(-x, -y, lim);
if(x < 0) return -bigmul(-x, y, lim);
if(y < 0) return -bigmul(x, -y, lim);
return y == 0 or x <= lim / y ? x * y : lim;
}
template <class T> T POW(T x, int n) {
T res = 1;
for(; n; n >>= 1, x *= x)
if(n & 1) res *= x;
return res;
}
template <class T, class S> T POW(T x, S n, const ll &mod) {
T res = 1;
x %= mod;
for(; n; n >>= 1, x = x * x % mod)
if(n & 1) res = res * x % mod;
return res;
}
vector<pll> factor(ll x) {
vector<pll> ans;
for(ll i = 2; i * i <= x; i++)
if(x % i == 0) {
ans.push_back({i, 1});
while((x /= i) % i == 0) ans.back().second++;
}
if(x != 1) ans.push_back({x, 1});
return ans;
}
template <class T> vector<T> divisor(T x) {
vector<T> ans;
for(T i = 1; i * i <= x; i++)
if(x % i == 0) {
ans.pb(i);
if(i * i != x) ans.pb(x / i);
}
return ans;
}
template <typename T> void zip(vector<T> &x) {
vector<T> y = x;
UNIQUE(y);
for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); }
}
template <class S> void fold_in(vector<S> &v) {}
template <typename Head, typename... Tail, class S> void fold_in(vector<S> &v, Head &&a, Tail &&...tail) {
for(auto e : a) v.emplace_back(e);
fold_in(v, tail...);
}
template <class S> void renumber(vector<S> &v) {}
template <typename Head, typename... Tail, class S> void renumber(vector<S> &v, Head &&a, Tail &&...tail) {
for(auto &&e : a) e = lb(v, e);
renumber(v, tail...);
}
template <class S, class... Args> vector<S> zip(vector<S> &head, Args &&...args) {
vector<S> v;
fold_in(v, head, args...);
sort(all(v)), v.erase(unique(all(v)), v.end());
renumber(v, head, args...);
return v;
}
template <typename S> void rearrange(const vector<S> &id) {}
template <typename S, typename T> void rearrange_exec(const vector<S> &id, vector<T> &v) {
vector<T> w(v.size());
rep(i, si(id)) w[i] = v[id[i]];
v.swap(w);
}
// 並び替える順番, 並び替える vector 達
template <typename S, typename Head, typename... Tail> void rearrange(const vector<S> &id, Head &a, Tail &...tail) {
rearrange_exec(id, a);
rearrange(id, tail...);
}
template <typename T> vector<T> RUI(const vector<T> &v) {
vector<T> res(v.size() + 1);
for(int i = 0; i < v.size(); i++) res[i + 1] = res[i] + v[i];
return res;
}
template <typename T> void zeta_supersetsum(vector<T> &f) {
int n = f.size();
for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b] += f[b | i];
}
template <typename T> void zeta_subsetsum(vector<T> &f) {
int n = f.size();
for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b | i] += f[b];
}
template <typename T> void mobius_subset(vector<T> &f) {
int n = f.size();
for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b] -= f[b | i];
}
template <typename T> void mobius_superset(vector<T> &f) {
int n = f.size();
for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b | i] -= f[b];
}
// 反時計周りに 90 度回転
template <typename T> void rot(vector<vector<T>> &v) {
if(empty(v)) return;
int n = v.size(), m = v[0].size();
vector<vector<T>> res(m, vector<T>(n));
rep(i, n) rep(j, m) res[m - 1 - j][i] = v[i][j];
v.swap(res);
}
vector<int> counter(const vector<int> &v, int max_num = -1) {
if(max_num == -1) max_num = MAX(v);
vector<int> res(max_num + 1);
fore(e, v) res[e]++;
return res;
}
// x in [l, r)
template <class T, class S> bool inc(const T &x, const S &l, const S &r) { return l <= x and x < r; }
template <class T, class S> bool inc(const T &x, const pair<S, S> &p) { return p.first <= x and x < p.second; }
// 便利関数
constexpr ll ten(int n) { return n == 0 ? 1 : ten(n - 1) * 10; }
constexpr ll tri(ll n) { return n * (n + 1) / 2; }
// l + ... + r
constexpr ll tri(ll l, ll r) { return (l + r) * (r - l + 1) / 2; }
ll max(int x, ll y) { return max((ll)x, y); }
ll max(ll x, int y) { return max(x, (ll)y); }
int min(int x, ll y) { return min((ll)x, y); }
int min(ll x, int y) { return min(x, (ll)y); }
// bit 演算系
#define bit(i) (1LL << i) // (1 << i)
#define test(b, i) (b >> i & 1) // b の i bit 目が立っているか
ll pow2(int i) { return 1LL << i; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
// int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int lowbit(ull a) { return a == 0 ? 64 : __builtin_ctzll(a); }
// int allbit(int n) { return (1 << n) - 1; }
constexpr ll mask(int n) { return (1LL << n) - 1; }
// int popcount(signed t) { return __builtin_popcount(t); }
// int popcount(ll t) { return __builtin_popcountll(t); }
int popcount(uint64_t t) { return __builtin_popcountll(t); }
static inline uint64_t popcount64(uint64_t x) {
uint64_t m1 = 0x5555555555555555ll;
uint64_t m2 = 0x3333333333333333ll;
uint64_t m4 = 0x0F0F0F0F0F0F0F0Fll;
uint64_t h01 = 0x0101010101010101ll;
x -= (x >> 1) & m1;
x = (x & m2) + ((x >> 2) & m2);
x = (x + (x >> 4)) & m4;
return (x * h01) >> 56;
}
bool ispow2(int i) { return i && (i & -i) == i; }
ll rnd(ll l, ll r) { //[l, r)
#ifdef noimi
static mt19937_64 gen;
#else
static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
#endif
return uniform_int_distribution<ll>(l, r - 1)(gen);
}
ll rnd(ll n) { return rnd(0, n); }
template <class t> void random_shuffle(vc<t> &a) { rep(i, si(a)) swap(a[i], a[rnd(0, i + 1)]); }
int in() {
int x;
cin >> x;
return x;
}
ll lin() {
unsigned long long x;
cin >> x;
return x;
}
template <class T, class S> pair<T, S> operator-(const pair<T, S> &x) { return pair<T, S>(-x.first, -x.second); }
template <class T, class S> pair<T, S> operator-(const pair<T, S> &x, const pair<T, S> &y) { return pair<T, S>(x.fi - y.fi, x.se - y.se); }
template <class T, class S> pair<T, S> operator+(const pair<T, S> &x, const pair<T, S> &y) { return pair<T, S>(x.fi + y.fi, x.se + y.se); }
template <class T> pair<T, T> operator&(const pair<T, T> &l, const pair<T, T> &r) { return pair<T, T>(max(l.fi, r.fi), min(l.se, r.se)); }
template <class T, class S> pair<T, S> operator+=(pair<T, S> &l, const pair<T, S> &r) { return l = l + r; }
template <class T, class S> pair<T, S> operator-=(pair<T, S> &l, const pair<T, S> &r) { return l = l - r; }
// 開閉
template <class T> bool intersect(const pair<T, T> &l, const pair<T, T> &r) { return (l.se < r.se ? r.fi < l.se : l.fi < r.se); }
template <class T> vector<T> &operator++(vector<T> &v) {
fore(e, v) e++;
return v;
}
template <class T> vector<T> operator++(vector<T> &v, int) {
auto res = v;
fore(e, v) e++;
return res;
}
template <class T> vector<T> &operator--(vector<T> &v) {
fore(e, v) e--;
return v;
}
template <class T> vector<T> operator--(vector<T> &v, int) {
auto res = v;
fore(e, v) e--;
return res;
}
template <class T> void connect(vector<T> &l, const vector<T> &r) { fore(e, r) l.eb(e); }
template <class T> vector<T> operator+(const vector<T> &l, const vector<T> &r) {
vector<T> res(max(si(l), si(r)));
rep(i, si(l)) res[i] += l[i];
rep(i, si(r)) res[i] += r[i];
return res;
}
template <class T> vector<T> operator-(const vector<T> &l, const vector<T> &r) {
vector<T> res(max(si(l), si(r)));
rep(i, si(l)) res[i] += l[i];
rep(i, si(r)) res[i] -= r[i];
return res;
}
template <class T> vector<T> &operator+=(const vector<T> &l, const vector<T> &r) {
if(si(l) < si(r)) l.resize(si(r));
rep(i, si(r)) l[i] += r[i];
return l;
}
template <class T> vector<T> &operator-=(const vector<T> &l, const vector<T> &r) {
if(si(l) < si(r)) l.resize(si(r));
rep(i, si(r)) l[i] -= r[i];
return l;
}
template <class T> vector<T> &operator+=(vector<T> &v, const T &x) {
fore(e, v) e += x;
return v;
}
template <class T> vector<T> &operator-=(vector<T> &v, const T &x) {
fore(e, v) e -= x;
return v;
}
template <typename T> struct edge {
int from, to;
T cost;
int id;
edge(int to, T cost) : from(-1), to(to), cost(cost) {}
edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {}
constexpr bool operator<(const edge<T> &rhs) const noexcept { return cost < rhs.cost; }
edge &operator=(const int &x) {
to = x;
return *this;
}
operator int() const { return to; }
friend ostream operator<<(ostream &os, const edge &e) { return os << e.to; }
};
template <typename T> using Edges = vector<edge<T>>;
template <typename T = int> Edges<T> read_edges(int m, bool weighted = false) {
Edges<T> res;
res.reserve(m);
for(int i = 0; i < m; i++) {
int u, v, c = 0;
scan(u), scan(v), u--, v--;
if(weighted) scan(c);
res.eb(u, v, c, i);
}
return res;
}
using Tree = vector<vector<int>>;
using Graph = vector<vector<int>>;
template <class T> using Wgraph = vector<vector<edge<T>>>;
Graph getG(int n, int m = -1, bool directed = false, int margin = 1) {
Tree res(n);
if(m == -1) m = n - 1;
while(m--) {
int a, b;
cin >> a >> b;
a -= margin, b -= margin;
res[a].emplace_back(b);
if(!directed) res[b].emplace_back(a);
}
return res;
}
Graph getTreeFromPar(int n, int margin = 1) {
Graph res(n);
for(int i = 1; i < n; i++) {
int a;
cin >> a;
res[a - margin].emplace_back(i);
}
return res;
}
template <class T> Wgraph<T> getWg(int n, int m = -1, bool directed = false, int margin = 1) {
Wgraph<T> res(n);
if(m == -1) m = n - 1;
while(m--) {
int a, b;
T c;
scan(a), scan(b), scan(c);
a -= margin, b -= margin;
res[a].emplace_back(b, c);
if(!directed) res[b].emplace_back(a, c);
}
return res;
}
void add(Graph &G, int x, int y) { G[x].eb(y), G[y].eb(x); }
template <class S, class T> void add(Wgraph<S> &G, int x, int y, T c) { G[x].eb(y, c), G[y].eb(x, c); }
#define TEST \
INT(testcases); \
while(testcases--)
i128 abs(const i128 &x) { return x > 0 ? x : -x; }
istream &operator>>(istream &is, i128 &v) {
string s;
is >> s;
v = 0;
for(int i = 0; i < (int)s.size(); i++) {
if(isdigit(s[i])) { v = v * 10 + s[i] - '0'; }
}
if(s[0] == '-') { v *= -1; }
return is;
}
ostream &operator<<(ostream &os, const i128 &v) {
if(v == 0) { return (os << "0"); }
i128 num = v;
if(v < 0) {
os << '-';
num = -num;
}
string s;
for(; num > 0; num /= 10) { s.push_back((char)(num % 10) + '0'); }
reverse(s.begin(), s.end());
return (os << s);
}
namespace aux {
template <typename T, unsigned N, unsigned L> struct tp {
static void output(std::ostream &os, const T &v) {
os << std::get<N>(v) << (&os == &cerr ? ", " : " ");
tp<T, N + 1, L>::output(os, v);
}
};
template <typename T, unsigned N> struct tp<T, N, N> {
static void output(std::ostream &os, const T &v) { os << std::get<N>(v); }
};
} // namespace aux
template <typename... Ts> std::ostream &operator<<(std::ostream &os, const std::tuple<Ts...> &t) {
if(&os == &cerr) { os << '('; }
aux::tp<std::tuple<Ts...>, 0, sizeof...(Ts) - 1>::output(os, t);
if(&os == &cerr) { os << ')'; }
return os;
}
template <typename T, typename S, typename U> std::ostream &operator<<(std::ostream &os, const priority_queue<T, S, U> &_pq) {
auto pq = _pq;
vector<T> res;
while(!empty(pq)) res.emplace_back(pq.top()), pq.pop();
return os << res;
}
template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) {
if(&os == &cerr) { return os << "(" << p.first << ", " << p.second << ")"; }
return os << p.first << " " << p.second;
}
template <class Ch, class Tr, class Container> std::basic_ostream<Ch, Tr> &operator<<(std::basic_ostream<Ch, Tr> &os, const Container &x) {
bool f = true;
if(&os == &cerr) os << "[";
for(auto &y : x) {
if(&os == &cerr)
os << (f ? "" : ", ") << y;
else
os << (f ? "" : " ") << y;
f = false;
}
if(&os == &cerr) os << "]";
return os;
}
#define dump(...) static_cast<void>(0)
#define dbg(...) static_cast<void>(0)
void OUT() { cout << endl; }
template <class Head, class... Tail> void OUT(const Head &head, const Tail &...tail) {
cout << head;
if(sizeof...(tail)) cout << ' ';
OUT(tail...);
}
template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
template <class T, class S> constexpr pair<T, S> inf<pair<T, S>> = {inf<T>, inf<S>};
template <class T> void OUT2(const T &t, T INF = inf<T>, T res = -1) { OUT(t != INF ? t : res); }
template <class T> void OUT2(vector<T> &v, T INF = inf<T>, T res = -1) {
fore(e, v) if(e == INF) e = res;
OUT(v);
fore(e, v) if(e == res) e = INF;
}
template <class F> struct REC {
F f;
REC(F &&f_) : f(forward<F>(f_)) {}
template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }
};
template <class S> vector<pair<S, int>> runLength(const vector<S> &v) {
vector<pair<S, int>> res;
for(auto &e : v) {
if(res.empty() or res.back().fi != e)
res.eb(e, 1);
else
res.back().se++;
}
return res;
}
vector<pair<char, int>> runLength(const string &v) {
vector<pair<char, int>> res;
for(auto &e : v) {
if(res.empty() or res.back().fi != e)
res.eb(e, 1);
else
res.back().se++;
}
return res;
}
struct string_converter {
char start = 0;
char type(const char &c) const { return (islower(c) ? 'a' : isupper(c) ? 'A' : isdigit(c) ? '0' : 0); }
int convert(const char &c) {
if(!start) start = type(c);
return c - start;
}
int convert(const char &c, const string &chars) { return chars.find(c); }
template <typename T> auto convert(const T &v) {
vector<decltype(convert(v[0]))> ret;
ret.reserve(size(v));
for(auto &&e : v) ret.emplace_back(convert(e));
return ret;
}
template <typename T> auto convert(const T &v, const string &chars) {
vector<decltype(convert(v[0], chars))> ret;
ret.reserve(size(v));
for(auto &&e : v) ret.emplace_back(convert(e, chars));
return ret;
}
int operator()(const char &v, char s = 0) {
start = s;
return convert(v);
}
int operator()(const char &v, const string &chars) { return convert(v, chars); }
template <typename T> auto operator()(const T &v, char s = 0) {
start = s;
return convert(v);
}
template <typename T> auto operator()(const T &v, const string &chars) { return convert(v, chars); }
} toint;
template <class T, class F> T bin_search(T ok, T ng, const F &f) {
while(abs(ok - ng) > 1) {
T mid = ok + ng >> 1;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
template <class T, class F> T bin_search_double(T ok, T ng, const F &f, int iter = 80) {
while(iter--) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
struct Setup_io {
Setup_io() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
cout << fixed << setprecision(20);
}
} setup_io;
#endif
#pragma endregion
namespace fast_gcd {
using u64 = uint64_t;
using u32 = uint32_t;
__attribute__((target("bmi"))) constexpr u64 binary_gcd(u64 a, u64 b) {
if(a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a);
int m = __builtin_ctzll(b);
a >>= n;
b >>= m;
while(a != b) {
int m = __builtin_ctzll(a - b);
bool f = a > b;
u64 c = f ? a : b;
b = f ? b : a;
a = (c - b) >> m;
}
return a << min(n, m);
}
} // namespace fast_gcd
using fast_gcd::binary_gcd;
// q / p
struct frac {
template <typename T> static constexpr inline T gcd(const T a, const T b) { return (b == 0) ? a : gcd(b, a % b); }
ll q, p;
constexpr void simplify() {
if(p < 0) {
p *= -1;
q *= -1;
}
ll g = binary_gcd(q < 0 ? -q : q, p);
if(g) {
p /= g;
q /= g;
if(p == 0 and q < 0) q = 1;
}
}
constexpr frac(ll q = 0, ll p = 1) noexcept : q(q), p(p) { simplify(); }
static frac raw(ll _q, ll _p) {
frac f;
f.q = _q, f.p = _p;
return f;
}
constexpr bool operator<(const frac &r) const { return q * r.p < p * r.q; }
constexpr bool operator>(const frac &r) const { return q * r.p > p * r.q; }
constexpr bool operator<=(const frac &r) const { return q * r.p <= p * r.q; }
constexpr bool operator>=(const frac &r) const { return q * r.p >= p * r.q; }
template <class T> constexpr bool operator<(const T &r) const { return *this < frac(r); }
template <class T> constexpr bool operator>(const T &r) const { return *this > frac(r); }
constexpr bool operator==(const frac &r) const { return q * r.p == p * r.q; }
constexpr bool operator!=(const frac &r) const { return !((*this) == r); }
constexpr frac operator+() const noexcept { return *this; }
constexpr frac operator-() const noexcept { return frac(-q, p); }
constexpr frac operator+(const frac r) const noexcept { return frac(*this) += r; }
constexpr frac operator-(const frac r) const noexcept { return frac(*this) -= r; }
constexpr frac operator*(const frac r) const noexcept { return frac(*this) *= r; }
constexpr frac operator/(const frac r) const noexcept { return frac(*this) /= r; }
constexpr frac &operator+=(const frac &r) noexcept {
ll g = binary_gcd(p, r.p);
q = r.p / g * q + p / g * r.q;
p = p / g * r.p;
(*this).simplify();
return *this;
}
constexpr frac &operator-=(const frac &r) noexcept {
ll g = binary_gcd(p, r.p);
q = r.p / g * q - p / g * r.q;
p = p / g * r.p;
(*this).simplify();
return *this;
}
constexpr frac &operator*=(const frac &r) noexcept {
q *= r.q;
p *= r.p;
(*this).simplify();
return *this;
}
constexpr frac &operator/=(const frac &r) noexcept {
q *= r.p;
p *= r.q;
(*this).simplify();
return *this;
}
void print() {
long double tmp = (long double)q / (long double)p;
cout << tmp;
}
};
istream &operator>>(istream &is, frac &p) {
ll a;
is >> a;
p = frac(a, 1);
return is;
}
ostream &operator<<(ostream &os, const frac &r) { return os << 1.0 * r.q / r.p; }
struct SBTnode;
struct raw_sbtnode {
long long dep;
frac l, r;
raw_sbtnode() {
dep = 0;
l = frac::raw(0, 1), r = frac::raw(1, 0);
}
raw_sbtnode(const SBTnode &node);
void ladd(long long y) {
l.q += r.q * y;
l.p += r.p * y;
}
void radd(long long y) {
r.q += l.q * y;
r.p += l.p * y;
}
void move(bool dir, long long d) {
if(dir == false)
radd(d);
else
ladd(d);
}
frac val() { return frac::raw(l.q + r.q, l.p + r.p); }
operator frac() { return val(); }
};
struct SBTnode {
static constexpr bool L = false, R = true;
using Path = vector<pair<bool, long long>>;
Path path;
long long dep = 0;
frac lval = frac::raw(0, 1), rval = frac::raw(1, 0);
void ladd(long long y) {
lval.q += rval.q * y;
lval.p += rval.p * y;
}
void radd(long long y) {
rval.q += lval.q * y;
rval.p += lval.p * y;
}
frac val() { return frac::raw(lval.q + rval.q, lval.p + rval.p); }
operator frac() { return val(); }
// a / b
SBTnode(long long a = 1, long long b = 1) {
bool dir = a < b ? L : R;
if(dir == L) swap(a, b);
for(; b; dir = !dir) {
long long q = a / b, r = a % b;
move_down(dir, q - (!r));
a = b, b = r;
}
}
SBTnode(const frac &f) : SBTnode(f.q, f.p) {}
SBTnode(const Path &p) : SBTnode() {
for(const auto &[dir, d] : p) move_down(dir, d);
}
raw_sbtnode move_virtual(bool dir, long long d) {
raw_sbtnode res(*this);
res.move(dir, d);
return res;
}
void move_down(const pair<bool, long long> &p) { return move_down(p.first, p.second); }
void move_down(bool dir, long long d) {
if(!d) return;
if(empty(path) or path.back().first != dir) path.emplace_back(dir, 0);
path.back().second += d, dep += d;
if(dir == L)
radd(d);
else
ladd(d);
}
raw_sbtnode move_up_virtual(long long d) {
assert(d <= dep);
raw_sbtnode res(*this);
for(int i = (int)path.size() - 1; i >= 0; i--) {
auto &[dir, t] = path[i];
long long m = min(t, d);
res.move(dir, -m);
if(!(d -= m)) return res;
}
assert(0);
}
void move_up(long long d) {
assert(d <= dep);
while(d) {
auto &[dir, t] = path.back();
path.pop_back();
ll m = min(d, t);
dep -= m, d -= m;
if(dir == L)
radd(-m);
else
ladd(-m);
if(t > m) path.emplace_back(dir, t - m);
}
}
static SBTnode lca(const SBTnode &x, const SBTnode &y) {
SBTnode res;
const auto &px = x.path;
const auto &py = y.path;
for(int i = 0; i < px.size(); i++) {
if(i == py.size()) break;
if(px[i] == py[i])
res.move_down(px[i]);
else {
if(px[i].first == py[i].first) res.move_down(px[i].first, min(px[i].second, py[i].second));
break;
}
}
return res;
}
template <typename F> void bin_search(const F &f, long long max_p, long long max_q = -1) {
auto check = [&](bool dir, long long d) {
auto nxt = move_virtual(dir, d);
auto nl = (dir == L ? nxt.r : nxt.l);
return !(nl.p > max_p or (max_q != -1 and nl.q > max_q));
};
while(true) {
bool flag = f(*this);
bool dir = flag ? R : L;
if(!check(dir, 1)) break;
for(long long b = 1;; b <<= 1) {
if(!check(dir, b) or f(move_virtual(dir, b)) != flag) {
b /= 2;
long long c = 0;
while(b) {
if(check(dir, b + c) and f(move_virtual(dir, b + c)) == flag) c += b;
b /= 2;
}
move_down(dir, c + (check(dir, c + 1)));
break;
}
}
}
}
};
raw_sbtnode::raw_sbtnode(const SBTnode &node) : dep(node.dep), l(node.lval), r(node.rval) {}
// f(0 / 1) : true のとき、分母が max_p, 分子が max_q 以下(設定しなかったら制約は分母のみ) で (true, false) の組になるような分数 が lval, rval
template <typename F> SBTnode sbt_bin_search(const F &f, long long max_p, long long max_q = -1) {
SBTnode node;
node.bin_search(f, max_p, max_q);
return node;
}
// ax + b mod m の prefix minimum な x の情報
// x は log(m) 個の等差数列をなすので、変化点の座標と、その間の交差の vector を返す
// https://maspypy.com/library-checker-min-of-mod-of-linear
pair<vector<long long>, vector<long long>> mod_linear_prefix_minimum(long long a, long long b, long long m) {
if(a >= m) a %= m;
if(b >= m) b %= m;
if((a = m - a) == m) a = 0;
vector<long long> x, dx;
x.emplace_back(0);
long long X = 0, Y = b;
long long g = gcd(a, m);
SBTnode node = sbt_bin_search([&](frac f) { return f <= frac::raw(a, m); }, m / g);
auto path = node.path;
SBTnode tmp;
if(long long c = a * tmp.lval.p - m * tmp.lval.q; c <= Y) {
if(c == 0) return {x, dx};
long long k = Y / c;
x.emplace_back(X += tmp.lval.p * k);
dx.emplace_back(tmp.lval.p);
Y -= c * k;
}
for(int i = 0; i < path.size(); i++) {
auto &[dir, d] = path[i];
if(dir == SBTnode::L)
tmp.move_down(dir, d);
else {
if(frac f = tmp.move_virtual(SBTnode::R, d).l; a * f.p - m * f.q <= Y) {
long long t = ceil(a * tmp.lval.p - m * tmp.lval.q - Y, m * tmp.rval.q - a * tmp.rval.p);
if(t < 0) assert(0);
tmp.move_down(dir, t);
long long c = a * tmp.lval.p - m * tmp.lval.q;
if(c == 0) break;
if(c < 0) assert(0);
long long k = Y / c;
x.emplace_back(X += tmp.lval.p * k);
dx.emplace_back(tmp.lval.p);
Y -= c * k;
if(t < d) {
d -= t;
i--;
}
} else {
tmp.move_down(dir, d);
}
}
}
return {x, dx};
}
// min ax + b mod m (0 <= x < n)
long long min_mod_linear(long long a, long long b, long long m, long long n) {
auto [x, dx] = mod_linear_prefix_minimum(a, b, m);
ll tx = 0;
if(x.back() < n)
tx = x.back();
else {
int i = lower_bound(begin(x), end(x), n) - begin(x) - 1;
tx = x[i] + (n - 1 - x[i]) / dx[i] * dx[i];
}
return (a * tx + b) % m;
}
vector<int> mobius(int n) {
vector<int> mu(n + 1, 1), p(n + 1, 1);
for(int i = 2; i <= n; i++) {
if(p[i] == 1) {
for(int j = i; j <= n; j += i) p[j] = i;
}
if((i / p[i]) % p[i] == 0)
mu[i] = 0;
else
mu[i] = -mu[i / p[i]];
}
return mu;
}
#include <atcoder/math>
int main() {
auto mob = mobius(310000);
TEST {
LL(n, k);
auto cnt = [&](frac f) {
ll res = 0;
rep(g, 1, n + 1) {
if(mob[g] == 0) continue;
ll s = 0;
rep(i, g, n + 1, g) { s += min(n, f.q * i / f.p) / g; }
// dump(g, s);
res += s * mob[g];
}
// dump(f.p, f.q, res);
return res;
// ll ma = ceil(f.p * (n + 1), f.q) - 1;
// if(ma < 0)
// ma = 0;
// else
// chmin(ma, n);
// ll res = atcoder::floor_sum(ma, f.p, f.q, f.q);
// res += n * (n - ma);
return res;
};
auto f = [&](frac f) { return cnt(f) <= k; };
auto node = sbt_bin_search(f, n, n);
auto v = node.lval;
if(cnt(v) < k)
OUT(-1);
else
cout << v.q << "/" << v.p << endl;
}
}
// int main() {
// dump("here");
// auto f = frac::raw(3, 6);
// OUT(f.q, f.p);
// exit(0);
// TEST {
// LL(n, a, b);
// ll g = gcd(a, b);
// ll k = bin_search(0LL, inf<ll>, [&](ll x) { return x - 1 - (i128(a) * x - 1 + b - g) / b <= n; });
// ll c = bin_search(b - g, -1LL, [&](ll x) { return (i128(a) * k - 1 + b - g) / b == (i128(a) * k - 1 + x) / b; });
// }
// }