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.
def emerald(st,d):
    
    if d==0 or st==0:
        return 0
    elif d==st and d%2==0:
        return d//2
    elif d==st and d%2!=0:
        return d//2+1
    elif st>d:
        if d<=st//2:
            return d
        elif d==st//2+1:
            return st//2
        else:
            return st//2+1
    else:
        if st<=d//2:
            return st
        elif st==d//2+1:
            return d//2
        else:
            return d//2+1


num = int(input())
for i in range(num):
    s,d=map(int, input().split())
    print(emerald(s,d))
    
