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())

def main():
    a,b = tuple(map(int, input().split()))
    
    if a>=2*b or b>=2*a:
        print(min(a,b))
        
    else:
        x = a//3
        y = b//3
        triplet = min(x,y)
        if triplet == x and a<b:
            a = a%3
            b = b-(3*triplet)
            triplet = 2*triplet
            if a==0:
                print(triplet)
            elif a==1:
                if b>=2:
                    print(triplet+1)
                else:
                    print(triplet)
            else:
                if b>=4:
                    print(triplet+2)
                elif b>=2:
                    print(triplet+1)
                else:
                    print(triplet)
        
        
        else:
            b = b%3
            a = a-(3*triplet)
            triplet = 2*triplet
            if b==0:
                print(triplet)
            elif b==1:
                if a>=2:
                    print(triplet+1)
                else:
                    print(triplet)
            else:
                if a>=4:
                    print(triplet+2)
                elif a>=2:
                    print(triplet+1)
                else:
                    print(triplet)

                    
for _ in range(T):
    main()