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.

import java.util.*;
public class ab5 {
public static void main(String...strings)
   {
	Scanner scan=new Scanner(System.in);
   long t=scan.nextInt();
   while(t-->0)
   {
        long a,b;
		 a=scan.nextLong();
		 b=scan.nextLong();
		 long p=Math.min(a,b);
		 long q=Math.max(a,b);
				
		 if(2*p<=q)
		{
    	  System.out.println(p);
		}
		else
		{
			System.out.println((p+q)/3);
		    
		}
       
   }
  
}
}
