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...":



Can you provide a Python code to find all values of k such that exactly k breaks could happen during the match between Alice and Borys in total?
assistant
#Here is Python code to find all values of k such that exactly k breaks could happen during the match between Alice and Borys in total.
 def run():
    n = int(input())
    for i in range (n):
        a,b = input().split(' ')
        a = int(a)
        b = int(b)
        min1 = 999999
        max1 = 0
        na = a+b-int((a+b)/2)
        for x in range(max (na-b, 0) ,min(a, na)+1,1 ):

            
            brks = na + a - 2*x
            if brks < 0:
                break
            #print (brks)
            if brks<min1:
                min1 = brks
            if brks > max1:
                max1 = brks
        if (a+b)%2==0:
            L = [i for i in range (min1, max1+2, 2)]
            L.sort()
            print(len(L))
            printp(L)
            
        else:
            min2 = 999999
            max2 = 0
            na = a+b-na
            for x in range(max (na - b, 0), min(a, na) +1,1 ):
                
                brks = na + a - 2*x
                if brks < 0:
                    break
                #print (brks)
                if brks<min2:
                    min2 = brks
                if brks > max2:
                    max2 = brks
            
            L = [i for i in range (min1, max1+2, 2)]
            K = [i for i in range (min2, max2+2, 2)] + L
            K.sort()
            print(len(K))
            printp(K)

def printp(X):
    for i in X:
        print(i, end = ' ')
    print()

run()