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
# sys.setrecursionlimit(100000)

# x = int(input())
# a = list(map(int, input().split()))

# f = open('input.txt')
# a = list(map(int, f.readline().split()))
# f.close()
# f = open('output.txt', 'w+')
# f.close()


def inp():
    return map(int, input().split())


for _ in range(int(input())):
    a, b = inp()
    a, b = min(a, b),  max(a, b)
    if a * 2< b:
        print(a)
        continue
    x = b // 2
    a -= x
    b = b % 2
    y = 0
    if b == 1 and a > 1:
        y += 1
        b -= 1
        a -= 2
    res = x + y + min(x, a // 3)
    print(res)
