Polycarp plays a well-known computer game (we won't mention its name). In this game, he can craft tools of two types — shovels and swords. To craft a shovel, Polycarp spends two sticks and one diamond; to craft a sword, Polycarp spends two diamonds and one stick.

Each tool can be sold for exactly one emerald. How many emeralds can Polycarp earn, if he has a sticks and b diamonds?

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

The only line of each test case contains two integers a and b (0 ≤ a, b ≤ 10^9) — the number of sticks and the number of diamonds, respectively.

Output

For each test case print one integer — the maximum number of emeralds Polycarp can earn.

Example

Input


4
4 4
1000000000 0
7 15
8 7


Output


2
0
7
5

Note

In the first test case Polycarp can earn two emeralds as follows: craft one sword and one shovel.

In the second test case Polycarp does not have any diamonds, so he cannot craft anything.


def f(inp):
    sticks = int(inp[0])
    diam = int(inp[1])
    shovels = 0
    swords = 0

    while diam > 0 and sticks > 0:
        if sticks >= diam and sticks > 1:
            shovels += 1
            sticks -= 2
            diam -= 1
        elif diam > 1:
            swords += 1
            sticks -= 1
            diam -= 2
        else:
            break

    print(shovels + swords)

def f2(inp):
    sticks = int(inp[0])
    diam = int(inp[1])
    res = 0

    if sticks == 0 or diam == 0:
        return res

    low = min([sticks, diam])
    high = max([sticks, diam])

    diff = high - low
    if diff > low: diff = low
    
    if diff > 2:
        res += diff
        low -= diff
        high -= 2*diff
    
    if low == 0 or high == 0:
        return res
        
    if high%2 == 0 and high == low:
        res += int(high/2)
    else:
        res += int(high/2) + 1

    return res 
    

    
        
            
    


if __name__ == "__main__":
    test = input()
    for e in range(int(test)):
        print(f2(input().split(" ")))