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! */
//devanshjsr

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 Solution
{
    	
	public static void main (String[] args) throws java.lang.Exception
	{
		 BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    StringTokenizer st=new StringTokenizer(br.readLine());
	    
		int t=Integer.parseInt(st.nextToken());
		
		while(t>0)
		{
		    st=new StringTokenizer(br.readLine());
		    int a=Integer.parseInt(st.nextToken());
		    int b=Integer.parseInt(st.nextToken());
		    
		    int ans=0;
		    
		    if(a==0 || b==0)
		    {
		        ans=0;
		    }
		    else
		    {
		        if(a>b)
		        {
		            int v1=(int)Math.min((a-b),b);
		            
		            b=b-v1;
		            a=a-2*v1;
		            
		            
		            int v2=(int)Math.min(a/3,b/3);
		            
		            a=a-v2*3;
		            b=b-v2*3;
		            
		            if(a==2)
		            {
		                if(b>=1)
		                {
		                    ans++;
		                }
		            
		            }
		            else if(a==1)
		            {
		                if(b>=2)
		                {
		                    ans++;
		                }
		            }
		            
		            ans+=(v1+v2*2);
		            
		        }
		        else
		        {
		            
		            int v1=(int)Math.min((b-a),a);
		            
		            a=a-v1;
		            b=b-2*v1;
		            
		            
		            int v2=(int)Math.min(a/3,b/3);
		            
		            a=a-v2*3;
		            b=b-v2*3;
		            
		            if(a==2)
		            {
		                if(b>=1)
		                {
		                    ans++;
		                }
		            
		            }
		            else if(a==1)
		            {
		                if(b>=2)
		                {
		                    ans++;
		                }
		            }
		            
		            ans+=(v1+v2*2);
		        }
		    }
		    
		     System.out.println(ans);
		    
		    t--;
		}
		
	}
}