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 count_z(S, a, b):
    a -= S
    b -= 2 * S
    return S + min(b, a // 2)

def ternary_search(a, b):
    left = 0
    right = min(a, b // 2)
    while right > left + 2:
        p1 = left  +  (right - left) // 3
        p2 = left + (2 * (right - left)) // 3
        if count_z(p1, a, b) > count_z(p2, a, b):
            right = p2
        else:
            left = p1
    res = 0
    for i in range(left, right + 1):
        res = max(res, count_z(i, a, b))
    return res



def main():
    t = int(input())
    for _ in range(t):
        a, b = tuple(map(int, input().split()))
        res = ternary_search(a, b)
        print(res)


if __name__ == '__main__':
    main()