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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/**
 * I realized that you might have doubt in this question, so if at some point in my 
 * code you find anything that you don't understand, please do not disturb me.
 *
 *                                                                 - Sheldon Cooper
 */

public class Sheldon {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        PrintWriter pw = new PrintWriter(System.out);
        
        try {
            int t = Integer.parseInt(br.readLine());
            while(t-->0) {
                st = new StringTokenizer(br.readLine());
                int n = Integer.parseInt(st.nextToken());
                int m = Integer.parseInt(st.nextToken());
                int min = Math.min(n, m);
                int max = Math.max(n, m);

                if(2*min <= max) {
                    pw.println(min);
                }
                else {
                    pw.println((n+m)/3);
                }

            }
        }
        finally {
            pw.flush();
            pw.close();
        }
    }
}
