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.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

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

    static class DMinimumEulerCycle {
        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int t = in.scanInt();
            loop:
            while (t-- > 0) {
                int n = in.scanInt();
                long l = in.scanLong();
                long r = in.scanLong();
                long m = r - l + 1;
                long last = (long) n * (n - 1) + 1;
                if (m == 1 && l == r && r == last) {
                    out.println(1);
                    continue loop;
                }


                int arr[] = new int[n + 1];
                long pre[] = new long[n + 1];
                arr[1] = (n - 1) * 2;
                for (int i = 2; i <= n; i++) arr[i] = arr[i - 1] - 2;
                for (int i = 1; i <= n; i++) pre[i] = arr[i] + pre[i - 1];
                int a = 0;
                for (int i = 1; i <= n - 1; i++) if (pre[i] < l) a = i;
                a++;
                long next = l - pre[a - 1];
                long b = a + ((next / 2) + (next % 2));
                int turn = (int) (l % 2);

                for (int i = 0; i < m; i++) {
                    if (i == m - 1 && r == last) {
                        out.print(1);
                        break;
                    }
                    if (turn == 1) {
                        out.print(a + " ");
                    } else {
                        out.print(b + " ");
                        b++;
                        if (b == (n + 1)) {
                            a++;
                            b = a + 1;
                        }
                    }
                    turn ^= 1;
                }

                out.println();

                // 1 2 1 3 2 3
//            1 2 1 3 1 4 1 5 2 3 2 4 2 5 3 4 3 5 4 5

            }
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int INDEX;
        private BufferedInputStream in;
        private int TOTAL;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (INDEX >= TOTAL) {
                INDEX = 0;
                try {
                    TOTAL = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (TOTAL <= 0) return -1;
            }
            return buf[INDEX++];
        }

        public int scanInt() {
            int I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

        public long scanLong() {
            long I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

    }
}