Problem: We have a secret array. You don't know this array and you have to restore it. However, you know some facts about this array:

  * The array consists of n distinct positive (greater than 0) integers. 
  * The array contains two elements x and y (these elements are known for you) such that x < y. 
  * If you sort the array in increasing order (such that a_1 < a_2 < … < a_n), differences between all adjacent (consecutive) elements are equal (i.e. a_2 - a_1 = a_3 - a_2 = … = a_n - a_{n-1}). 



It can be proven that such an array always exists under the constraints given below.

Among all possible arrays that satisfy the given conditions, we ask you to restore one which has the minimum possible maximum element. In other words, you have to minimize max(a_1, a_2, ..., a_n).

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

The only line of the test case contains three integers n, x and y (2 ≤ n ≤ 50; 1 ≤ x < y ≤ 50) — the length of the array and two elements that are present in the array, respectively.

Output

For each test case, print the answer: n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of the required array. If there are several answers, you can print any (it also means that the order of elements doesn't matter).

It can be proven that such an array always exists under the given constraints.

Example

Input


5
2 1 49
5 20 50
6 20 50
5 3 8
9 13 22


Output


1 49 
20 40 30 50 10
26 32 20 38 44 50 
8 23 18 13 3 
1 10 13 4 19 22 25 16 7 

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.LinkedHashSet;
import java.util.Set;

public class YetAnotherArrayRestoration {
	static BufferedReader in;
    static PrintWriter out;
 
    public static void main(String[] args) {
        try {
			readInput();
			solve();
		} catch (Exception e) {
			e.printStackTrace(System.err);
            System.exit(-1);
		}finally{
			 try {
				in.close();
			} catch (IOException e) {}
	         out.close();
		}
    }
 
    private static void solve() throws IOException {
    	in.lines().forEach(item -> {
    		String[] input = item.split(" ");
    		if(input.length > 1){
    			int countNumbers;
    			Integer x,y,n;
    			Set<Integer> result = new LinkedHashSet<>(); 
    			
    			n = new Integer(input[0]);
    			x = new Integer(input[1]);
    			y = new Integer(input[2]);
    			
    			result.add(x);
    			result.add(y);
    			
    			if(n == 2){
    				out.println(createFormattedResult(result));
					return;
    			}
    			
    			countNumbers = n-2;
    			
    			//Create numbers between x and y
    			int recorrence = getRecurrence(y - x, countNumbers);
    			if(recorrence != 0){
    				Integer element = new Integer(x);
    				while(true){
    					element = element + recorrence;
    					if(element >= y)
    						break;
    					
    					result.add(element);
    					countNumbers--;    					
    					if(countNumbers == 0){
    						out.println(createFormattedResult(result));
    						return;
    					}
    				}
    			}
    			
    			//Create numbers between 1 and x
    			Integer element = new Integer(x);
				while(true){
					element = element - recorrence;
					if(element < 1)
						break;
					
					result.add(element);
					countNumbers--;
					if(countNumbers == 0){
						out.println(createFormattedResult(result));
						return;
					}
				}
				
				//Create numbers from y
    			element = new Integer(y);
				while(true){
					element = element + recorrence;
					result.add(element);
					countNumbers--;
					if(countNumbers == 0){
						out.println(createFormattedResult(result));
						return;
					}
				}
    		}
    	  }
    	);
    }
    
    private static StringBuilder createFormattedResult(Set<Integer> result) {
    	StringBuilder resultFormatted = new StringBuilder();
    	result.forEach(item -> {
    		resultFormatted.append(item.toString() + " ");
    	});
    	
    	
    	return resultFormatted;
    }
    
    /**
     * Get the recurrence between numbers.
     * 
     * @param difference
     * @param numbersQuant
     * @return
     */
    private static int getRecurrence(Integer difference, int numbersQuant) {
    	int numbersQuantTemp = numbersQuant + 1;
    	while(difference % numbersQuantTemp != 0){
    		numbersQuantTemp--;
    	}
    	
    	return difference / numbersQuantTemp;
    }
    
    private static void readInput() throws FileNotFoundException {
    	if (System.getProperty("ONLINE_JUDGE") != null) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }
}