126 lines
3.0 KiB
C++
126 lines
3.0 KiB
C++
#include <cstdio>
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#include <cstdlib>
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#include <cstring>
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#include <cmath>
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#include <ctime>
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#include <iostream>
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#include <algorithm>
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#include <queue>
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#include <set>
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#include <map>
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#include <stack>
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#include <string>
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#include <vector>
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#include <deque>
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#include <list>
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#include <functional>
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#include <numeric>
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#include <cctype>
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using namespace std;
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inline int getflen(int n) {
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int t = (int)ceil(n / 2.0);
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return n - t + 1;
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}
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inline int getslen(int n) {
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int s1 = n % 2 == 0 ? (n - 1) : n;
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int t1 = (int)floor(n/3.0 + 1/3.0) * 2 + 1;
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int ans = (s1 - t1) / 2 + 1;
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int s2 = (int)floor(n / 2.0 + 1 / 2.0) - 1;
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int t2 = (int)ceil(n/3.0);
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ans += s2 - t2 + 1;
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return ans;
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}
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inline int gettlen(int n) {
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int s1 = n;
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while(s1 % 3 == 0) {
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s1--;
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}
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int t1 = (int)floor(n/4.0 + 1/4.0) * 3 + 2;
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int s3 = s1 - 1;
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int t3 = (int)floor(n/4.0 + 1/4.0) * 3 + 1;
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int s2 = (int)floor(n/3.0 + 1/3.0) * 2 - 1;
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int t2 = (int)floor(n/4.0 + 1/4.0) * 2 + 1;
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int s4 = (int)ceil(n/3.0) - 1;
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int t4 = (int)ceil(n/4.0);
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int ans = 0;
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if(s1 % 3 == 1) {
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ans += 2;
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s1 -= 2;
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s3 -= 2;
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s4 -= 1;
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}
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ans += (s1 - t1) / 3 + 1;
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ans += (s3 - t3) / 3 + 1;
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ans += (s2 - t2) / 2 + 1;
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ans += s4 - t4 + 1;
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return ans;
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}
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inline void get_f(int n, int k, int &a, int &b) {
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a = 1;
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b = n - k + 1;
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}
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inline void get_s(int n, int k, int &a, int &b) {
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int s1 = n % 2 == 0 ? (n - 1) : n;
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int s2 = (int)floor(n / 2.0 + 1 / 2.0);
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if(k % 2 == 1) {
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a = 2;
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b = s1 - k + 1;
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}else {
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a = 1;
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b = s2 - k / 2;
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}
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}
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inline void get_t(int n, int k, int &a, int &b) {
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int s1 = n;
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while(s1 % 3 == 0) {
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s1--;
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}
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int s2 = (int)floor(n/3.0 + 1/3.0) * 2 - 1;
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int s3 = (s1 % 3 == 2) ? (s1 - 1) : (s1 - 2);
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int s4 = (int)ceil(n/3.0) - 1;
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if(k % 4 == 1) {
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a = 3;
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b = s1 - (k - 1) / 4 * 3;
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}else if(k % 4 == 3) {
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a = 3;
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b = s3 - (k - 3) / 4 * 3;
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}else if((k % 4 == 2) xor (s1 % 3 == 2)) {
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a = 1;
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if(k % 4 == 2) {
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b = s4 - (k - 2) / 4;
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}else {
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b = s4 - (k - 4) / 4;
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}
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}else {
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a = 2;
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if(k % 4 == 2) {
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b = s2 - (k - 2) / 4 * 2;
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}else {
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b = s2 - (k - 4) / 4 * 2;
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}
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}
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}
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pair<int, int> get_farey(int n, int k) {
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pair<int, int> ret;
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int fl = getflen(n);
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int sl = getslen(n);
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if(k <= fl) {
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get_f(n, k, ret.first, ret.second);
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}else if(k <= sl + fl) {
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get_s(n, k - fl, ret.first, ret.second);
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}else {
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get_t(n, k - fl - sl, ret.first, ret.second);
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}
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return ret;
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}
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int main() {
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int T, n, k;
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scanf("%d", &T);
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while(T--) {
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scanf("%d%d", &n, &k);
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pair<int, int> ans = get_farey(n, k);
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printf("%d/%d\n", ans.first, ans.second);
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}
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return 0;
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}
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