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())

def _check_response(a,b):
    a,b = max(a,b), min(a,b)
    diff = a-b
    c = min(b, diff)
    a -=2*c
    b -= c
    c += 2 * ( b // 3)
    b1 = b % 3
    a -= 3*(b//3)
    if a == 0 or b1 == 0:
        return c
    if a == 1 and b1 == 1:
        return c
    if a >= 2 and b1 == 1:
        return c+1
    if b1 == 2 and a >= 1:
        return c+1


for _ in range(t):
    a, b = tuple(map(int, input().split()))
    c = _check_response(a,b) 
    print(c)


