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()

    if a > p:
        a, p = p, a

    if p == 0 or a == 0:
        print(0)
    else:
        if p > 2*a:
            ans = a
        elif a > 2*p:
            ans = p
        else:
            par = min(int(p/3), int(a/3))

            ans = 2* par
            p -= 3*par
            a -= 3*par

            while (p > 0 and a > 1) or (p > 1 and a > 0):
                if p >= a:
                    # создаём лопату
                    p -= 2
                    a -= 1
                    ans += 1
                else:
                # создаём меч
                    p -= 1
                    a -= 2
                    ans += 1

        print(ans)


