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())
i=0
while(i<t):
    summer=0
    n,m=list(map(int,input().split()))
    mini=min(n,m)
    maxi=max(n,m)
    def spl(n):
        return 2*(n//3)+(n%3)//2

    
    if(maxi>=2*mini):
        print(mini)
    else:
        print(maxi-mini+spl(2*mini-maxi))

        # summer+=2*(mini//3)
        # leftmin=mini%3
        # leftmax=maxi-((mini//3)*3)

        # if(leftmin==0):
        #     print(summer)
        # elif(leftmin==1):
        #     if(leftmax>=2):
        #         print(summer+1)
        #     else:
        #         print(summer)
        # else:
        #     if(leftmax>=4):
        #         print(summer+2)
        #     else:
        #         print(summer+1)
                
        



    i+=1