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 PYTHON3):

Solution:
import math
import re
import itertools
import copy
import time
import sys


def input_linear(lamb=lambda x: int(x), seperator=" "):
    return map(lamb, input().split(seperator))


def input_array(lamb=lambda x: int(x), seperator=" "):
    return list(map(lamb, input().split(seperator)))


def input_matrix(rows, lamb=lambda x: int(x), seperator=" "):
    tmp_matrix = []
    for i in range(rows):
        tmp_matrix.append(input_array(lamb, seperator))
    return tmp_matrix


def input_graph_al_pair(vertices, lines, lamb=lambda x: int(x), seperator=" ", directional=False, remove_dup=False):
    temp_matrix = [x[:] for x in [[]]*vertices]
    if not directional:
        if not remove_dup:
            for i in range(lines):
                ina, inb = input_linear(lamb, seperator)
                temp_matrix[ina].append(inb)
                temp_matrix[inb].append(ina)
        else:
            for i in range(lines):
                ina, inb = input_linear(lamb, seperator)
                if inb not in temp_matrix[ina]: temp_matrix[ina].append(inb)
                if ina not in temp_matrix[inb]: temp_matrix[inb].append(ina)
        return temp_matrix
    else:
        if not remove_dup:
            for i in range(lines):
                ina, inb = input_linear(lamb, seperator)
                temp_matrix[ina].append(inb)
        else:
            for i in range(lines):
                ina, inb = input_linear(lamb, seperator)
                if inb not in temp_matrix[ina]: temp_matrix[ina].append(inb)
        return temp_matrix


# MAIN
if __name__ == '__main__':
    for _ in range(int(input())):
        curr = [0, 0, math.inf, 0]
        n, x, y = input_linear()
        if x == y:
            print(" ".join(list(map(str, [x] * n))))
        if x > y: x, y = y, x
        else:
            for a1 in range(0, n-1):
                for a2 in range(a1+1, n):
                    if (y - x) % (a2-a1) != 0:
                        continue
                    d = (y - x)/(a2 - a1)
                    sta = x - a1 * d
                    if sta <= 0:
                        continue
                    if sta + (n-1) * d < curr[2]:
                        curr = [a1, a2, sta + (n-1) * d, sta, d]
                    #print([a1, a2, sta + (n-1) * d, sta, d])
        dod = int(curr[4])
        star = int(curr[3])
        for i in range(n):
            print(star + dod * i, end=" ")
        print("")