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.nio.file.LinkOption;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main implements Runnable {




    public long ans(long a , long b){
        return Math.min((a+b)/3,Math.min(a,b));
    }


    
    
    public void solve() throws Exception {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        long t = sc.nextLong();
        while (t>0){
            long a = sc.nextLong();
            long b = sc.nextLong();
            out.println(ans(a,b));
            t--;
        }

    }









//////////////main function...................................................................//
    public static PrintWriter out;
    ////....\\\\
    public static void main(String[] args) throws Exception {
        new Thread(null, new Main(), "", 1 << 26).start();
    }

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }


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

        boolean hasNextInt() {
            return true;
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

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

    }

    public void run() {
        try {
            solve();
        } catch (Exception ex) {
            throw new RuntimeException(ex);
        } finally {
            out.close();
        }
    }
}