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.*;
import java.util.ArrayList;
import java.math.BigInteger; 
 
public class Main{   
     static class Pair{
     int x;
     int y;
       Pair(){
       
       }
       Pair(int x,int y){
       this.x=x;
       this.y=y;
       }
     }
    
 
    public static void main(String[] args)
    {
    Scanner param = new Scanner(System.in);
    
    int end=param.nextInt();
    while(end-->0)
    {
         long n=param.nextLong();
         long m=param.nextLong();
         long max=Math.max(n,m);
         long min=Math.min(n,m);
         long sum=0;
       
        long sum2=0;
        
        
            sum2=(max+min)/3;
        
        System.out.println(Math.min(sum2,min));
    }
    //8 7
    //7 7-->1
    //4 5-->2
    //3 3-->3
    //1 2-->4
    
    
    
}
}
