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.
import math


def main():
    t = int(input())
    for case in range(t):
        s, d = input().split()
        s = int(s)
        d = int(d)
        count = 0
        if d > s:
            big = d
            small = s
        else:
            big = s
            small = d
        if big >= 2 * small:
            count = small
        else:
            while big > 3 and small > 2:
                temp = int(big / 2)
                if temp % 2 == 1:
                    temp -= 1
                big -= temp
                small -= temp / 2
                count += temp / 2
                if big < small:
                    temp = big
                    big = int(small)
                    small = int(temp)
            if big == 3 and small == 3:
                count += 2
            elif small > 0 and big > 1:
                count += 1
        print(int(count))


if __name__ == '__main__':
    main()
