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, stdout
"""
    n = stdin.readline()
    arr = [int(x) for x in stdin.readline().split()]
    stdout.write(str(summation))
"""
for test in range(int(stdin.readline())):
    arr = [int(x) for x in stdin.readline().split()]
    a = arr[0]
    b = arr[1]

    if a>=2*b or b>=2*a :
        stdout.write(str(min(a,b))+"\n")

    else :
        ans1 = max(a,b)-min(a,b)
        a = min(a,b)-ans1

        ans = a//3
        left = a-(3*ans)

        if left==0 or left==1:
            stdout.write(str(2*ans +ans1)+"\n")
        else :
            stdout.write(str((2*ans)+1+ans1)+"\n")