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.
from sys import stdin
input = iter(stdin.readlines()).__next__

def em(a, b):
    if b == 0:
        return 0
    if b == 1:
        return int(a > 1)
    if b == 2:
        return 2 if a >= 4 else 1
    if a >= 2 * b:
        return b
    if a == b:
        e = a // 3 * 2
        res = e // 2 * 3
        return e + em(a - res, b - res)
    
    diff = a - b
    e = diff
    a -= diff * 2
    b -= diff
    return e + em(max(a, b), min(a, b))
        

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

    print(em(max(a, b), min(a, b)))

    