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:
import java.io.*;
import java.util.StringTokenizer;

public class Main {
    
    public static void main(String[] args) throws IOException {
        Scanner scn = new Scanner(System.in);
        OutputWriter out = new OutputWriter(System.out);
        // Always print a trailing "\n" and close the OutputWriter as shown at the end of your output
        
        // example:
        int t=scn.nextInt();
        for(int i1=0;i1<t;i1++){
            int n=scn.nextInt();long l=scn.nextLong();long r=scn.nextLong();
            long max=(long)(n)*(n-1)+1;
            if(l==max){
                out.print(1+" ");continue;
            }
            long i=binroot(n,l);
            long b=2*n*(i-1)-(i-1)*i;
            long b1=2*n*(i)-(i+1)*i;
            while(l<=r){
                if(l==max){
                    out.print(1+" ");break;
                }
                if((l-b)%2==0){
                    out.print((i+(l-b)/2)+" ");
                }
                else{
                    out.print(i+" ");
                }
                l++;
                if(l>b1){
                    i++;b=b1;b1+=2*n-2*i;
                }
            }
            out.print("\n");
            
        }
        out.close();
    }
    public static long binroot(long n,long l1){
        long l=0;long r=n-1;
        while(r-l>1){
            long m=(l+r)/2;
            if((2*n-1-m)*m<l1){
                l=m;
            }
            else{
                r=m;
            }
        }
        return(r);
    }
    // fast input
    static class Scanner {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public Scanner(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String line = reader.readLine();
                    if (line == null)
                        return null;
                    tokenizer = new StringTokenizer(line);
                } catch (Exception e) {
                    throw(new RuntimeException());
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() { return Integer.parseInt(next()); }
        public long nextLong() { return Long.parseLong(next()); }
        public double nextDouble() { return Double.parseDouble(next()); }
    }

    // fast output
    static class OutputWriter {
        BufferedWriter writer;

        public OutputWriter(OutputStream stream) {
            writer = new BufferedWriter(new OutputStreamWriter(stream));
        }

        public void print(int i) throws IOException { writer.write(i); }
        public void print(String s) throws IOException { writer.write(s); }
        public void print(char[] c) throws IOException { writer.write(c); }
        public void close() throws IOException { writer.close(); }
    }


}