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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author bhavy seth
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, InputReader sc, PrintWriter out) {
            int t = sc.nextInt();
            while (t-- > 0) {
                int n = sc.nextInt();
                long l = sc.nextLong();
                long r = sc.nextLong();
                long count = 0;
                int start = 0;
                for (int i = 1; i <= n; i++) {
                    long x = Math.max(1, (n - i) * 2);
                    if (l <= count + x) {
                        start = i;
                        break;
                    } else {
                        count += x;
                    }
                }

        /*  if(l==count+1){
              out.print(start+" ");
              count++;
          }*/
                int curr = start;
                long incnt = 0;
                {
                    for (int i = 0; i < Math.max(2 * (n - start), 1); i++) {
                        count++;
                        incnt++;
                        if (incnt % 2 == 0) {
                            curr++;
                        }
                        if (count == l) {
                            break;
                        }
                    }
                    if (incnt % 2 == 0) {
                        for (int i = curr; i <= n; i++) {
                            if (count <= r) {
                                out.print(i + " ");
                                count++;
                            }
                            if (i == n)
                                break;
                            if (count <= r) {
                                out.print(start + " ");
                                count++;
                            }
                            if (count > r)
                                break;
                        }
                    } else {
                        for (int i = curr + 1; i <= n; i++) {
                            if (count <= r) {
                                out.print(start + " ");
                                count++;
                            }
                            if (count <= r) {
                                out.print(i + " ");
                                count++;
                            }
                            if (count > r)
                                break;
                        }
                    }

                    if (count < r) {
                        for (int i = start + 1; i < n; i++) {
                            for (int j = i + 1; j <= n; j++) {
                                if (count <= r) {
                                    out.print(i + " ");
                                    count++;
                                }
                                if (count <= r) {
                                    out.print(j + " ");
                                    count++;
                                }
                                if (count > r)
                                    break;
                            }
                            if (count > r)
                                break;
                        }

                    }
                    if (count <= r)
                        out.print(1);
                }

                out.println();
            }
        }

    }

    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream inputStream) {
            br = new BufferedReader(new
                    InputStreamReader(inputStream));
        }

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

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

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}