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.
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{

	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc=new Scanner(System.in);
		int T = sc.nextInt();
        for(int t=0;t<T;t++)
        {
            int a = sc.nextInt();
            int b = sc.nextInt();
            int count=0;
            if(a==0 || b==0)
            {
                System.out.println(0);
            }
            else if(2*a<=b)
            System.out.println(a);
            else if(2*b<=a)
            System.out.println(b);
            else if(a<b)
            {
                count = (int)Math.ceil((2*a-b)/(double)3);
                count = count + (a - 2*count); 
                System.out.println(count);
            }
            else
            {
                count = (int)Math.ceil((2*b-a)/(double)3);
                count = count + (b - 2*count);
                System.out.println(count);
            }

            
            
            
        } //ques 1
        
	}
}


