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.io.*;
import java.util.*;
import java.lang.*;
 
 
public class Main{
    public static void main(String[] args) {
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int T = in.nextInt();
        for(int test=0;test<T;test++){
            long a = in.nextInt();
            long b = in.nextInt();
            if(b<a){
                long tmp = a;
                a=b;
                b=tmp;
            }
            long x = Math.min(b-a,a);
            a-=x;
            b-=(2*x);
            //out.println("x1:"+x);
            if(a>0){
                x+=((a/3)*2);
                if(a%3==2) x++;
            }
            out.println(x);
        }

        out.close();
   }

     

   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
}