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 Codeforces_Prac;
import java.util.*;
import java.io.*;
public class Shovel_Swords {
    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
        
        public FastReader(){
            br=new BufferedReader(new InputStreamReader(System.in));
        }

        String next(){
            while(st==null || !st.hasMoreElements()){
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (Exception e) {
                
                    e.printStackTrace();
                }

            }
            return st.nextToken();
        }

        int nextInt(){
            return Integer.parseInt(next());
        }

        String nextLine(){
            String str="";
            try {
                str=br.readLine();
            } catch (Exception e) {
                  e.printStackTrace();
            }
            return str;
        }

        long nextLong(){
            return Long.parseLong(next());
        }

    }
  public static void main (String []  args){
      FastReader in = new FastReader ();
      int t = in.nextInt();
      while(t-- > 0){
          long a = in.nextLong();
          long b = in.nextLong();
          long c = (a + b)/3;
          long ans = Math.min(Math.min(a,b),c);
          System.out.println(ans);
      }
  }
}
