Problem: You are given a complete directed graph K_n with n vertices: each pair of vertices u ≠ 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, ..., 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}, ..., v_r.

Input

The first line contains the single integer T (1 ≤ T ≤ 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 ≤ n ≤ 10^5, 1 ≤ l ≤ r ≤ n(n - 1) + 1, r - l + 1 ≤ 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.

Output

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

Example

Input


3
2 1 3
3 3 6
99995 9998900031 9998900031


Output


1 2 1 
1 3 2 3 
1 

Note

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.

Solution (in JAVA):

Solution:
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
If I'm the sun, you're the moon
Because when I go up, you go down
*******************************
I'm working for the day I will surpass you
https://www.a2oj.com/Ladder16.html
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class x1334D
   {
      public static void main(String omkar[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int T = Integer.parseInt(st.nextToken());
         StringBuilder sb = new StringBuilder();
         outer:while(T-->0)
         {
            st = new StringTokenizer(infile.readLine());
            int N = Integer.parseInt(st.nextToken());
            long L = Long.parseLong(st.nextToken());
            long R = Long.parseLong(st.nextToken());
            long val = 0L;
            for(int i=1; i < N; i++)
            {
               if(val+2*(N-i) >= L)
               {
                  long startdex = val+1;
                  R -= startdex;
                  L -= startdex;
                  ArrayList<Integer> ls = new ArrayList<Integer>();
                  ls.add(i);
                  int next = i+1;
                  for(int a=1; a < 2*(N-i); a++)
                  {
                     if(a%2 == 1)
                        ls.add(next++);
                     else
                        ls.add(i);
                  }
                  int boof = i;
                  while(boof+1 < N && ls.size() <= R)
                  {
                     ls.add(boof+1);
                     next = boof+2;
                     for(int a=1; a < 2*(N-boof-1); a++)
                     {
                        if(a%2 == 1)
                           ls.add(next++);
                        else
                           ls.add(boof+1);
                     }
                     boof++;
                  }
                  if(boof+1 >= N)
                     ls.add(1);
                  //print
                  for(int a = (int)L; a <= R; a++)
                     sb.append(ls.get(a)+" ");
                  sb.append("\n");
                  continue outer;
               }
               else
                  val += 2*(N-i);
            }
            sb.append("1\n");
         }
         System.out.print(sb);
      }
   }