Minimum Euler Cycle

题意翻译

求 $n$ 个点的完全有向图的最小字典序欧拉回路的第 $l$ 到 $r$ 个节点。

题目描述

You are given a complete directed graph $ K_n $ with $ n $ vertices: each pair of vertices $ u \neq v $ in $ K_n $ have both directed edges $ (u, v) $ and $ (v, u) $ ; there are no self-loops. You should find such a cycle in $ K_n $ that visits every directed edge exactly once (allowing for revisiting vertices). We can write such cycle as a list of $ n(n - 1) + 1 $ vertices $ v_1, v_2, v_3, \dots, v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 $ — a visiting order, where each $ (v_i, v_{i + 1}) $ occurs exactly once. Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists. Since the answer can be too large print its $ [l, r] $ segment, in other words, $ v_l, v_{l + 1}, \dots, v_r $ .

输入输出格式

输入格式

The first line contains the single integer $ T $ ( $ 1 \le T \le 100 $ ) — the number of test cases. Next $ T $ lines contain test cases — one per line. The first and only line of each test case contains three integers $ n $ , $ l $ and $ r $ ( $ 2 \le n \le 10^5 $ , $ 1 \le l \le r \le n(n - 1) + 1 $ , $ r - l + 1 \le 10^5 $ ) — the number of vertices in $ K_n $ , and segment of the cycle to print. It's guaranteed that the total sum of $ n $ doesn't exceed $ 10^5 $ and the total sum of $ r - l + 1 $ doesn't exceed $ 10^5 $ .

输出格式

For each test case print the segment $ v_l, v_{l + 1}, \dots, v_r $ of the lexicographically smallest cycle that visits every edge exactly once.

输入输出样例

输入样例 #1

3
2 1 3
3 3 6
99995 9998900031 9998900031

输出样例 #1

1 2 1 
1 3 2 3 
1

说明

In the second test case, the lexicographically minimum cycle looks like: $ 1, 2, 1, 3, 2, 3, 1 $ . In the third test case, it's quite obvious that the cycle should start and end in vertex $ 1 $ .

题意翻译

求 $n$ 个点的完全有向图的最小字典序欧拉回路的第 $l$ 到 $r$ 个节点。