human
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.
 def f(a,b) :
    m=0
    l=[]
    if (a+b)%2==0 :
        if a==0 or b==0 :
            m=1
            l.append((a+b)//2)
        else :
            var=abs(a-b)//2
            for i in range(min(a,b)+1) :
                m=m+1
                l.append(var+2*i)
    else :
        if a==0 or b==0 :
            m=2
            l.append((a+b)//2)
            l.append((a+b+1)//2)
        else :
            var1=abs(a-b)//2
            var2=var1+1
            var=min(a,b)
            m=(var+1)*2
            for i in range(m) :
                l.append(var1+i)
    return (m,l)
            

t=int(input())
i=0
while i != t :
    i=i+1
    x=input().split(" ")
    a=int(x[0])
    b=int(x[1])
    (m,l)=f(a,b)
    print(m)
    print(*l)