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.util.Scanner;

public class Minimum_eularC_ycle {
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		while (t-- > 0) {
			long n = s.nextLong();
			long l = s.nextLong();
			long r = s.nextLong();
			long k = 1;
			long sum = 0;
			while (true && k < n) {
				sum += 2 * (n - k);
				k++;
				if (sum >= l) {
					k--;
					sum-=2 * (n - k);
					break;
				}

			}

			
			while (sum < r && k <= n) {
				long sub = 1 + k;
				for (int i = 1; i <= 2 * (n - k) && sum < r ; i++) {
					sum++;

					if (sum >= l) {
						if (i % 2 == 1) {
							System.out.print(k + " ");
						} else {
							System.out.print(sub + " ");
						}
						
					}
					if(i%2==0)
						sub++;

				}
				k++;
			}
			if(sum+1==r)
				System.out.print(1+" ");
			System.out.println();
		}
	}
}