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.
from sys import stdin,stdout
def main():
    for t in range(int(stdin.readline())):
        s,d=map(int,stdin.readline().split())
        if s==0 or d==0:
            print(0)
        else:
            flag=0
            a=0
            if (2*s-d)>0 and (2*d-s)>0:
                a=(s+d)//3
                flag=1
            #print(flag)
            if flag==1:
                b=max(d//2,s//2)
                print(max(a,b))
            else:
                if (2*s-d)<=0:
                    print(s)
                else:
                    print(d)
if __name__=="__main__":
    main() 