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.
import sys
from math import log2, floor

TEST = 0

if TEST == 1:
    input_file = open("inputA.txt", "r")
    input_from_file = input_file.readlines()

def read_int():
    if TEST:
        return int(input_from_file.pop(0))
    else:
        return int(sys.stdin.readline())

def read_ints():
    if TEST:
        return list(map(int, input_from_file.pop(0).rstrip().split()))
    else:
        return list(map(int, sys.stdin.readline().split()))


t = read_int()


for test in range(t):
    p, a = read_ints()

    ans = min(a, p, int((a+p)/3))

    print(ans)


