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.
"""
n = int(input())
for _ in range(n):
    a, b = map( int, input().split() )
    count = 0
    if (a > 0 and b ==0) or (a == 0 and b > 0):
        print('0')
    elif a < b and ( b >= a * 2):
        print( a )
    elif b < a and (a >= 7*2):
        print( b )
    else:
        while (a >= 1 and b >= 2) or (a >= 2 and b >= 1) :
            if a > b:
                a = a - 2
                b = b - 1
                count += 1
            else:
                a = a - 1
                b = b - 2
                count += 1
        print( count )
"""
for _ in range(int(input())):
    a,b = map(int,input().split())
    print(min(min(a,b),(a+b)//3))

