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.Scanner;

public class Main {

    public static void main(String[] args) {
	// write your code here
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        while(t-->0){
            int stick   = scanner.nextInt();
            int diamond = scanner.nextInt();
            int count=0;
            while(stick>0 && diamond>0){
                if(stick<2 && diamond<2) break;
                if(stick==diamond){
                    count+=Math.ceil(stick/2);
                    break;
                }
                else if (stick > diamond) {
                    int dif=stick-diamond;
                    if(dif>=diamond){
                        count+=diamond;
                        break;
                    }
                    stick-=2*dif;
                    diamond-=dif;
                    count+=dif;
                }
                else{
                    int dif=diamond-stick;
                    if(dif>=stick){
                        count+=stick;
                        break;
                    }
                    stick-=dif;
                    diamond-=2*dif;
                    count+=dif;
                }
                count++;
            }
            System.out.println(count);
        }
    }
}