結果

問題 No.2262 Fractions
ユーザー heno239heno239
提出日時 2023-04-07 21:42:45
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,279 ms / 2,000 ms
コード長 7,254 bytes
コンパイル時間 2,260 ms
コンパイル使用メモリ 153,068 KB
実行使用メモリ 30,952 KB
最終ジャッジ日時 2024-05-05 07:21:50
合計ジャッジ時間 39,351 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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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 723 ms
30,848 KB
testcase_01 AC 253 ms
30,952 KB
testcase_02 AC 233 ms
30,820 KB
testcase_03 AC 241 ms
30,892 KB
testcase_04 AC 247 ms
30,848 KB
testcase_05 AC 244 ms
30,848 KB
testcase_06 AC 282 ms
30,820 KB
testcase_07 AC 253 ms
30,824 KB
testcase_08 AC 240 ms
30,824 KB
testcase_09 AC 251 ms
30,720 KB
testcase_10 AC 262 ms
30,720 KB
testcase_11 AC 677 ms
30,820 KB
testcase_12 AC 672 ms
30,824 KB
testcase_13 AC 678 ms
30,848 KB
testcase_14 AC 671 ms
30,828 KB
testcase_15 AC 676 ms
30,740 KB
testcase_16 AC 379 ms
30,820 KB
testcase_17 AC 384 ms
30,820 KB
testcase_18 AC 373 ms
30,824 KB
testcase_19 AC 970 ms
30,848 KB
testcase_20 AC 908 ms
30,720 KB
testcase_21 AC 971 ms
30,824 KB
testcase_22 AC 882 ms
30,820 KB
testcase_23 AC 786 ms
30,824 KB
testcase_24 AC 1,165 ms
30,820 KB
testcase_25 AC 1,168 ms
30,720 KB
testcase_26 AC 1,103 ms
30,820 KB
testcase_27 AC 1,148 ms
30,720 KB
testcase_28 AC 1,219 ms
30,816 KB
testcase_29 AC 1,279 ms
30,720 KB
testcase_30 AC 1,254 ms
30,796 KB
testcase_31 AC 1,231 ms
30,820 KB
testcase_32 AC 1,260 ms
30,848 KB
testcase_33 AC 1,253 ms
30,820 KB
testcase_34 AC 1,199 ms
30,816 KB
testcase_35 AC 1,193 ms
30,820 KB
testcase_36 AC 1,217 ms
30,692 KB
testcase_37 AC 92 ms
30,720 KB
testcase_38 AC 80 ms
30,720 KB
testcase_39 AC 990 ms
30,820 KB
testcase_40 AC 945 ms
30,948 KB
testcase_41 AC 947 ms
30,812 KB
testcase_42 AC 1,026 ms
30,792 KB
testcase_43 AC 969 ms
30,820 KB
testcase_44 AC 1,160 ms
30,696 KB
testcase_45 AC 1,167 ms
30,720 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function 'void query(int, ll)':
main.cpp:325:14: warning: 'ansy' may be used uninitialized [-Wmaybe-uninitialized]
  325 |         ansy /= g;
      |         ~~~~~^~~~
main.cpp:280:18: note: 'ansy' was declared here
  280 |         ll ansx, ansy;
      |                  ^~~~
In function 'll gcd(ll, ll)',
    inlined from 'void query(int, ll)' at main.cpp:323:13:
main.cpp:165:16: warning: 'ansx' may be used uninitialized [-Wmaybe-uninitialized]
  165 |         while (b) {
      |                ^
main.cpp: In function 'void query(int, ll)':
main.cpp:280:12: note: 'ansx' was declared here
  280 |         ll ansx, ansy;
      |            ^~~~

ソースコード

diff # 

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
//ll mod = 1;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

using ld = long double;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
template<typename T>
vector<T> vmerge(vector<T>& a, vector<T>& b) {
	vector<T> res;
	int ida = 0, idb = 0;
	while (ida < a.size() || idb < b.size()) {
		if (idb == b.size()) {
			res.push_back(a[ida]); ida++;
		}
		else if (ida == a.size()) {
			res.push_back(b[idb]); idb++;
		}
		else {
			if (a[ida] < b[idb]) {
				res.push_back(a[ida]); ida++;
			}
			else {
				res.push_back(b[idb]); idb++;
			}
		}
	}
	return res;
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
//mod should be <2^31
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
	return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
	a = a + b; return a;
}
mP operator-(mP a, mP b) {
	return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
	a = a - b; return a;
}
LP operator+(LP a, LP b) {
	return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
	a = a + b; return a;
}
LP operator-(LP a, LP b) {
	return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
	a = a - b; return a;
}

mt19937 mt(time(0));

const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
//int dx[4] = { 1,0,-1,0 };
//int dy[4] = { 0,1,0,-1 };

//-----------------------------------------


const int mn = 300005;
bool isp[mn];
vector<int> pch[mn];
vector<int> ps;

vector<ll> num(mn);
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		pch[i].push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
			pch[j].push_back(i);
		}
	}
	num[1] = 0;
	for (int i = 2; i < mn; i++) {
		int cop = i;
		for (auto p : pch[i]) {
			cop /= p; cop *= p - 1;
		}
		num[i] = num[i - 1] + cop;
	}
}

void query(int n, ll k) {
	ll s = 2 * num[n] + 1;
	if (k >= s) {
		cout << -1 << "\n"; return;
	}
	if (k == num[n]) {
		cout << 1 << "/" << 1 << "\n"; return;
	}
	bool rev = false;
	if (k > num[n]) {
		rev = true;
		k = 2 * num[n] - k;
	}
	ll ansx, ansy;

	auto calc = [&](ld x) {
		ll res = 0;
		for (int i = 2; i <= n; i++) {
			int ri = i * x;
			//[1,ri]
			int num = 0;
			int sz = pch[i].size();
			rep(j, (1 << sz)) {
				int coef = 1;
				int pro = 1;
				rep(k, sz) {
					if (j & (1 << k)) {
						pro *= pch[i][k];
						coef *= -1;
					}
				}
				num += coef * (ri / pro);
			}
			res += num;
		}
		//cout << x << " " << res << "\n";
		return res;
	};
	//cout << calc(1) << " " << num[n] << "\n";
	ld l = 0, r = 1;
	rep(_, 50) {
		ld mid = (l + r) / 2;
		if (calc(mid) <= k)l = mid;
		else r = mid;
	}
	ld mi = INF;
	for (int i = 2; i <= n; i++) {
		int t = i * r;
		ld val = (ld)t / i;
		ld dif = abs(r - val);
		if (dif < mi) {
			mi = dif;
			ansx = t, ansy = i;
		}
	}
	//cout << "? " << r << "\n";
	int g = gcd(ansx, ansy);
	ansx /= g;
	ansy /= g;
	if (rev)swap(ansx, ansy);
	cout << ansx << "/" << ansy << "\n";
}

void solve() {
	int n; ll k; cin >> n >> k; k--;
	query(n, k);
}



signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(12);
	//init_f();
	init();
	//while(true)
	//expr();
	int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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