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.
t = int(input())

for i in range(t):
    a, b = map(int, input().split())
    if a == 0 or b == 0:
        c = 0
    elif a > b:
        x = a/b
        if x >= 2:
            c = b
        elif x > 1:
            p = (2*b -a)/3
            b = b -2*p
            # print(p, b)
            c = p + b
    elif b > a:
        x = b/a
        if x >= 2:
            c = a
        elif x > 1:
            p = (2*a -b)/3
            a = a -2*p
            c = p + a
    else:
        c = 2*(a//3) + ((a%3)/2)
    print(int(c))