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 = input()
t = int(t)

def solve(a, b):
    k = 0
    if a==0 or b==0:
        print(0)
        return

    if a>b :
        a, b = b, a
    
    if b>=2*a:
        k += a
    else :
        k += (b-a)
        k += ((2*a-b)//3)*2

        if (2*a-b)%3==2:
            k+=1

    # while(a>=2 and b>=2):   
    #     if a<=b:
    #         a-=1
    #         b-=2
    #         k+=1
    #     else :
    #         a-=2
    #         b-=1
    #         k+=1

    # if a>=2 and b==1:
    #     k+=1
    # elif a==1 and b>=2:
    #     k+=1

    print(k)
    

for i in range(t):
    a, b = map(int, input().split())
    solve(a, b)