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 time import time
#from random import randint

def function(a, b):
    cash = 0
    a, b = max(a,b), min(a,b)
    #7 = 3x + 1 = > x = (7 - 1) / 3
    while (a > 2 and b > 2 and a < 2*b):
        a -= 3
        b -= 3
        cash += 2
    cash += min(a//2, b)
    print(cash)

def solve(a, b):
    print(min(a, b, (a+b)//3))

def submit():
    for _ in range(int(input())):
        a, b = list(map(int, input().split()))
        solve(a, b)

def tryOut():
    #start = time()
    a, b = 8, 7
    function(a, b)
    #print(time()-start)

submit()