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:
// package com.company;
import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class CH4 {
    public static void main(String[] Args){
        FastReader scan=new FastReader();
        int t=scan.nextInt();
        StringBuilder fp=new StringBuilder();
        while(t-->0){
            long n=scan.nextInt();
            long l=scan.nextLong();
            long r=scan.nextLong();
            StringBuilder print=new StringBuilder();
            long cur=0;
            boolean lf=false;
            long ib=-1;
            for(long i=1;i<n;i++){
                long tba=(n-i)*2;
                if(cur+tba<l){
                    cur+=tba;
                }else{
//                    System.out.println(i);
                    long fa=l-cur;
                    if(fa%2!=0&&l<=r){
                        print.append(i+" ");
                        fa++;
                        l++;
                    }
                    if(fa%2==0&&l<=r){
                        print.append((i+fa/2)+" ");
                        l++;
                    }
                    long rem=(tba-fa)/2;
                    for(long j=n-rem+1;j<=n&&l<=r;j++){
                        print.append(i+" ");
                        l++;
                        if(l<=r){
                            print.append(j+" ");
                            l++;
                        }
                    }
                    ib=i+1;
                    break;
                }
            }
            if(l<=r){
                for(long i=ib;ib!=-1&&i<n&&l<=r;i++){
                    long j=i+1;
                    while(j<=n){
                        if(l<=r){
                            print.append(i+" ");
                            l++;
                        }
                        if(l<=r){
                            print.append(j+" ");
                            l++;
                        }
                        j++;
                    }
                }
                if(l<=r){
                    print.append(1);
                }
            }
            fp.append(print+"\n");
        }
        System.out.println(fp);
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }
// 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

}