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())
for i in range(t):
    a,b = map(int, input().strip().split(' '))
    if a==0 or b==0:
        print(0)
    elif a>=2*b or b>=2*a:
        print(min(a,b))
    else:
        if a>b:
            m1=a   #m1 is max and 
            m2=b   #m2 is min    
        else:
            m1=b
            m2=a
        k=m1-m2
        m=m1-2*k
        if m%3==0 or m%3==1:
            m=k+((m//3)*2)
            print(m)
        else:
            m=k+((m//3)*2)+1
            print(m)
        
            
    