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.
from sys import stdin, stdout

def main():
    tests = []
    N = int(stdin.readline())

    tests = [ [int(l[0]), int(l[1])] for l in [stdin.readline().rstrip('\n').split(' ') for i in range(N)]]

    answers = []
    for test in tests:
        a, b = test
        if a == 0 or b == 0:
            answers.append(0)
        else:
            sols = []
            sols.append(min(a, b//2))
            sols.append(min(a//2, b))
            x = (2*a -b) // 3
            y = (2*b -a) // 3
            if x >=0 and y >= 0:
                sols.append((a + b)//3)

            answers.append(max(sols))

    for answer in answers:
        stdout.write(str(answer) + '\n')
    return 0

if __name__ == '__main__':
    main()
