結果
| 問題 |
No.2262 Fractions
|
| コンテスト | |
| ユーザー |
 Nachia
|
| 提出日時 | 2023-04-07 23:36:01 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 404 ms / 2,000 ms |
| コード長 | 6,283 bytes |
| コンパイル時間 | 1,213 ms |
| コンパイル使用メモリ | 89,104 KB |
| 最終ジャッジ日時 | 2025-02-12 03:03:56 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 45 |
ソースコード
#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\divisor-convolution.hpp"
#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\prime-sieve-explicit.hpp"
#include <vector>
#include <algorithm>
#include <cassert>
#include <iostream>
namespace nachia{
namespace prime_sieve_explicit_internal{
std::vector<bool> isprime = { false }; // a[x] := isprime(2x+1)
void CalcIsPrime(int z){
if((int)isprime.size() *2+1 < z+1){
int new_z = isprime.size();
while(new_z*2+1 < z+1) new_z *= 2;
z = new_z-1;
isprime.resize(z+1, true);
for(int i=1; i*(i+1)*2<=z; i++) if(isprime[i]){
for(int j=i*(i+1)*2; j<=z; j+=i*2+1) isprime[j] = false;
}
}
}
std::vector<int> prime_list = {2};
int prime_list_max = 0;
void CalcPrimeList(int z){
while((int)prime_list.size() < z){
if((int)isprime.size() <= prime_list_max + 1) CalcIsPrime(prime_list_max + 1);
for(int p=prime_list_max+1; p<(int)isprime.size(); p++){
if(isprime[p]) prime_list.push_back(p*2+1);
}
prime_list_max = isprime.size() - 1;
}
}
void CalcPrimeListUntil(int z){
if(prime_list_max < z){
CalcIsPrime(z);
for(int p=prime_list_max+1; p<(int)isprime.size(); p++){
if(isprime[p]) prime_list.push_back(p*2+1);
}
prime_list_max = isprime.size() - 1;
}
}
}
bool IsprimeExplicit(int n){
using namespace prime_sieve_explicit_internal;
if(n == 2) return true;
if(n % 2 == 0) return false;
CalcIsPrime(n);
return isprime[(n-1)/2];
}
int NthPrimeExplicit(int n){
using namespace prime_sieve_explicit_internal;
CalcPrimeList(n);
return prime_list[n];
}
int PrimeCountingExplicit(int n){
using namespace prime_sieve_explicit_internal;
if(n < 2) return 0;
CalcPrimeListUntil(n);
auto res = std::upper_bound(prime_list.begin(), prime_list.end(), n) - prime_list.begin();
return (int)res;
}
// [l, r)
std::vector<bool> SegmentedSieveExplicit(long long l, long long r){
assert(0 <= l); assert(l <= r);
long long d = r - l;
if(d == 0) return {};
std::vector<bool> res(d, true);
for(long long p=2; p*p<=r; p++) if(IsprimeExplicit(p)){
long long il = (l+p-1)/p, ir = (r+p-1)/p;
if(il <= p) il = p;
for(long long i=il; i<ir; i++) res[i*p-l] = false;
}
if(l < 2) for(long long p=l; p<2 && p<r; p++) res[l-p] = false;
return res;
}
} // namespace nachia
#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\divisor-convolution.hpp"
#line 8 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\divisor-convolution.hpp"
namespace nachia{
template<class Elem>
void DivisorZeta(std::vector<Elem>& a){
using namespace prime_sieve_explicit_internal;
int n = a.size() - 1;
for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i*d] += a[i];
}
template<class Elem>
void DivisorInvZeta(std::vector<Elem>& a){
using namespace prime_sieve_explicit_internal;
int n = a.size() - 1;
for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i] += a[i*d];
}
template<class Elem>
void DivisorMobius(std::vector<Elem>& a){
using namespace prime_sieve_explicit_internal;
int n = a.size() - 1;
for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i*d] -= a[i];
}
template<class Elem>
void DivisorInvMobius(std::vector<Elem>& a){
using namespace prime_sieve_explicit_internal;
int n = a.size() - 1;
for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i] -= a[i*d];
}
template<class Elem>
std::vector<Elem> GcdConvolution(std::vector<Elem> a, std::vector<Elem> b){
assert(a.size() == b.size());
assert(1 <= a.size());
DivisorInvZeta(a);
DivisorInvZeta(b);
for(int i=1; i<(int)a.size(); i++) a[i] *= b[i];
DivisorInvMobius(a);
return a;
}
template<class Elem>
std::vector<Elem> LcmConvolution(std::vector<Elem> a, std::vector<Elem> b){
assert(a.size() == b.size());
assert(1 <= a.size());
DivisorZeta(a);
DivisorZeta(b);
for(int i=1; i<(int)a.size(); i++) a[i] *= b[i];
DivisorMobius(a);
return a;
}
}
#line 2 "..\\Main.cpp"
#line 4 "..\\Main.cpp"
#include <string>
#line 7 "..\\Main.cpp"
#include <atcoder/modint>
using namespace std;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;
using Modint = atcoder::static_modint<998244353>;
pair<i64,i64> testcase(){
i64 N, K; cin >> N >> K;
__int128_t l = 0, r = ((__int128_t)1ll << 96) + 1;
while(l+1 < r){
__int128_t m = (l+r)/2;
vector<i64> cnt(N+2);
for(i64 c=1; c<=N; c++){
i64 r = (m * c) >> 64;
r = min(r, N);
if(r > c){
cnt[c] += c;
cnt[c+1] -= c-1;
cnt[r+1] -= 1;
}
else{
cnt[c] += r;
cnt[c+1] -= r;
}
}
cnt[0] = 0;
for(int i=1; i<=N; i++) cnt[i] += cnt[i-1];
nachia::DivisorMobius(cnt);
i64 sumcnt = 0;
for(int i=1; i<=N; i++) sumcnt += cnt[i];
//cout << "q = " << ((double)((i64)(m >> 34)) * 0x1.p-30) << endl;
if(sumcnt < K) l = m; else r = m;
}
// l < x <= r
if(l == ((__int128_t)1ll << 96)) return {-1,-1};
i64 a = N+1, b = 1;
//cout << ((double)((i64)l) * 0x1.p-64) << endl;
for(int i=1; i<=N; i++){
i64 q = ((__int128_t)(l * i) >> 64) + 1;
if(q > N) continue;
//cout << "i = " << i << " , q = " << q << endl;
if(q * b < a * i){ a = q; b = i; }
}
return {a,b};
}
int main(){
int T; cin >> T;
rep(t,T){
auto ans = testcase();
if(ans.first < 0) cout << "-1\n"; else cout << ans.first << '/' << ans.second << '\n';
}
return 0;
}
struct ios_do_not_sync{
ios_do_not_sync(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
}
} ios_do_not_sync_instance;