human
Write me a Python program to find all values of k such that exactly k breaks could happen during the match between Alice and Borys in total given the following:
PYTHON3 solution for "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...":
assistant
#Here is Python program to find all values of k such that exactly k breaks could happen during the match between Alice and Borys in total.
 class Solver():
    def __init__(self):
        self._ans = []
        tc = int(input())
        for _ in range(tc):
            a, b = map(int, input().strip().split())
            ans = set()
            self._solve(a, b, (a + b + 1) // 2, (a + b) // 2, ans)
            self._solve(b, a, (a + b + 1) // 2, (a + b) // 2, ans)
            self._ans.append(sorted(ans))
        
        [print(len(ans),'\n', ' '.join(str(_) for _ in ans)) for ans in self._ans]

    def _solve(self, a, b, p, q, ans:set):
        for x in range(p+1):
            y = a - (p - x)
            if 0 <= y <= q:
                ans.add(x+y)

if __name__ == '__main__':
    Solver()