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.
t = int(input())
rez = []

for i in range(t):
    A = input().split(" ")
    m = int(A[0])
    l = int(A[1])
    if l == 0 or m == 0:
        rez.append(0)
    elif min(l,m)*2 <= max(l,m):
        rez.append(min(l,m))
    elif(m == l):
        rez.append(int(2*l//3))
    else:
        n = max(l,m) - min(l,m)
        rez.append(int(n + (max(l,m) - n/2)//3*2))


for i in  range(len(rez)):
    print(rez[i])