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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

      static class DMinimumEulerCycle {
            public void solve(int testNumber, InputReader in, OutputWriter out) {
                  int t = in.nextInt();
                  while (t-- > 0) {
                        int n = in.nextInt();
                        long l = in.nextLong();
                        long r = in.nextLong();
                        StringBuilder str = new StringBuilder();
                        long[] sum = new long[n];
                        sum[0] = 2 * (n - 1);
                        int mm = 2;
                        for (int i = 1; i < n; i++) {
                              int xx = n - mm;
                              sum[i] = sum[i - 1] + 2 * xx;
                              mm++;
                        }

                        while (l <= r) {
                              if (l == (1L * n * (n - 1) + 1)) {
                                    str.append("1 ");
                              } else {
                                    int start = 0;
                                    int end = n - 1;
                                    int ans = -1;
                                    while (start <= end) {
                                          int mid = (start + end) / 2;
                                          if (sum[mid] < l) {
                                                start = mid + 1;
                                          } else if (sum[mid] >= l) {
                                                ans = mid;
                                                end = mid - 1;
                                          }
                                    }

                                    long l1 = l;


                                    if (ans > 0)
                                          l = l - sum[ans - 1];

                                    String ss = "";
                                    if (l % 2 == 1) {
                                          ss = (1 + ans) + " ";
                                    } else {
                                          ss = (1 + ans + l / 2) + " ";
                                    }
                                    str.append(ss);

                                    l = l1;

                              }
                              l++;
                        }
                        out.printLine(str.toString());
                  }
            }

      }

      static class OutputWriter {
            private final PrintWriter writer;

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

            public OutputWriter(Writer writer) {
                  this.writer = new PrintWriter(writer);
            }

            public void print(Object... objects) {
                  for (int i = 0; i < objects.length; i++) {
                        if (i != 0) {
                              writer.print(' ');
                        }
                        writer.print(objects[i]);
                  }
            }

            public void printLine(Object... objects) {
                  print(objects);
                  writer.println();
            }

            public void close() {
                  writer.close();
            }

      }

      static class InputReader {
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;

            public InputReader(InputStream stream) {
                  this.stream = stream;
            }

            public int read() {
                  if (numChars == -1)
                        throw new InputMismatchException();

                  if (curChar >= numChars) {
                        curChar = 0;
                        try {
                              numChars = stream.read(buf);
                        } catch (IOException e) {
                              throw new InputMismatchException();
                        }
                        if (numChars <= 0)
                              return -1;
                  }

                  return buf[curChar++];
            }

            public int nextInt() {
                  int c = read();

                  while (isSpaceChar(c))
                        c = read();

                  int sgn = 1;

                  if (c == '-') {
                        sgn = -1;
                        c = read();
                  }

                  int res = 0;

                  do {
                        if (c < '0' || c > '9')
                              throw new InputMismatchException();

                        res *= 10;
                        res += c & 15;

                        c = read();
                  } while (!isSpaceChar(c));

                  return res * sgn;
            }

            public long nextLong() {
                  int c = read();

                  while (isSpaceChar(c))
                        c = read();

                  int sign = 1;

                  if (c == '-') {
                        sign = -1;

                        c = read();
                  }

                  long result = 0;

                  do {
                        if (c < '0' || c > '9')
                              throw new InputMismatchException();

                        result *= 10;
                        result += c & 15;

                        c = read();
                  } while (!isSpaceChar(c));

                  return result * sign;
            }

            public boolean isSpaceChar(int c) {
                  return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }

      }
}