Alice and Borys are playing tennis.

A tennis match consists of games. In each game, one of the players is serving and the other one is receiving.

Players serve in turns: after a game where Alice is serving follows a game where Borys is serving, and vice versa.

Each game ends with a victory of one of the players. If a game is won by the serving player, it's said that this player holds serve. If a game is won by the receiving player, it's said that this player breaks serve.

It is known that Alice won a games and Borys won b games during the match. It is unknown who served first and who won which games.

Find all values of k such that exactly k breaks could happen during the match between Alice and Borys in total.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^3). Description of the test cases follows.

Each of the next t lines describes one test case and contains two integers a and b (0 ≤ a, b ≤ 10^5; a + b > 0) — the number of games won by Alice and Borys, respectively.

It is guaranteed that the sum of a + b over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case print two lines.

In the first line, print a single integer m (1 ≤ m ≤ a + b + 1) — the number of values of k such that exactly k breaks could happen during the match.

In the second line, print m distinct integers k_1, k_2, …, k_m (0 ≤ k_1 < k_2 < … < k_m ≤ a + b) — the sought values of k in increasing order.

Example

Input


3
2 1
1 1
0 5


Output


4
0 1 2 3
2
0 2
2
2 3

Note

In the first test case, any number of breaks between 0 and 3 could happen during the match: 

  * Alice holds serve, Borys holds serve, Alice holds serve: 0 breaks; 
  * Borys holds serve, Alice holds serve, Alice breaks serve: 1 break; 
  * Borys breaks serve, Alice breaks serve, Alice holds serve: 2 breaks; 
  * Alice breaks serve, Borys breaks serve, Alice breaks serve: 3 breaks. 



In the second test case, the players could either both hold serves (0 breaks) or both break serves (2 breaks).

In the third test case, either 2 or 3 breaks could happen: 

  * Borys holds serve, Borys breaks serve, Borys holds serve, Borys breaks serve, Borys holds serve: 2 breaks; 
  * Borys breaks serve, Borys holds serve, Borys breaks serve, Borys holds serve, Borys breaks serve: 3 breaks. 
from sys import *
import math

# stdin = open('input.txt', 'r')

def solve_case(t):
    a, b = [int(x) for x in stdin.readline().rstrip().split()]
    total = a + b

    min_k = 0
    max_k = 0
    # a first
    a_ser = math.ceil((a + b) / 2)
    if a <= a_ser:
        min_k = a_ser - a
        max_k = a_ser + a
    else:
        min_k = a - a_ser
        max_k = b + total - a_ser


    #b first
    if total % 2 != 0:
        a_ser = math.floor((a + b) / 2)
        if a <= a_ser:
            min_k = min(min_k, a_ser - a)
            max_k = max(max_k, a_ser + a)
        else:
            min_k = min(min_k, a - a_ser)
            max_k = max(max_k, b + total - a_ser)

        print(max_k - min_k + 1)
        for k in range(min_k, max_k + 1):
            print(k, end= " ")
    else:
        arr = []
        for k in range(min_k, max_k + 1, 2):
            arr.append(k)

        print(len(arr))
        for k in arr:
            print(k, end= " ")
    print("")

def main():
    T = int(stdin.readline().rstrip())
    for t in range(T):
        solve_case(t)

main()
