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 emeralds(sticks,diamonds):
    if sticks*2 <= diamonds:
        return sticks
    elif diamonds*2 <= sticks:
        return diamonds
    else:
        return (sticks+diamonds)//3


def main():
    t=int(input())
    a=0
    while a<t:
        l=input().split()
        (sticks,diamonds)=(int(l[0]),int(l[1]))
        print(emeralds(sticks,diamonds))
        a=a+1


main()

