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 bisect
import collections
import functools
import itertools
import math
import heapq
import random
import string


def repeat(_func=None, *, times=1):
    def decorator(func):
        @functools.wraps(func)
        def wrapper(*args, **kwargs):
            for _ in range(times):
                func(*args, **kwargs)

        return wrapper

    if _func is None:
        return decorator
    else:
        return decorator(_func)


def unpack(func=int):
    return map(func, input().split())


def l_unpack(func=int):
    """list unpack"""
    return list(map(func, input().split()))


def s_unpack(func=int, rev=False):
    """sorted list unpack"""
    return sorted(map(func, input().split()), reverse=rev)


def ml_unpack(n):  # multiple line unpack
    """list of n integers passed on n line, one on each"""
    return [int(input()) for _ in range(n)]


def range_n():
    return range(int(input()))


def getint():
    return int(input())


def factor(n):
    d = {}
    while not n % 2:
        d[2] = d.get(2, 0) + 1
        n //= 2
    i = 3
    while i * i <= n:
        while not n % i:
            d[i] = d.get(i, 0) + 1
            n //= i
        i += 2
    if n > 1:
        d[n] = d.get(n, 0) + 1
    return d


def get_sum(a):
    """return sum of difference of all unique pairs"""
    ans = 0
    n = len(a)
    for i in range(n):
        # ans += (a[i] * i) - (n - i - 1) * a[i]
        ans += (i - (n - i - 1)) * a[i]
    return ans


@repeat(times=getint())
def main():
    n, x, y = unpack()
    ans = [0] * n
    p, q = 0, 0
    for i in range(n):
        for j in range(i + 1, n):
            if (not (y - x) % (j - i)) and j - i >= q - p:
                p, q = i, j

    d = (y - x) // (q - p)
    ans[p] = x
    for i in range(p - 1, -1, -1):
        ans[i] = ans[i + 1] - d
    for i in range(p + 1, n):
        ans[i] = ans[i - 1] + d
    if ans[0] <= 0:
        for i in range(n):
            if ans[i] <= 0:
                ans.append(ans[-1] + d)
            else:
                ans = ans[i:]
                break

    print(*ans)


main()