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;

/**
 * SwordsShovels
 */
public class SwordsShovels {

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        long versuche = s.nextLong();
        for (int i = 0; i < versuche; i++) {
            long dia = s.nextLong();
            long sticks = s.nextLong();
            System.out.println(getEarnableEmeralds(sticks, dia));
        }
    }

    public static long getEarnableEmeralds(long sticks, long diamonds){
        long emeralds = 0;
        while(!(sticks < 2 || diamonds < 2)){
            if(!(sticks == diamonds)){
                if(sticks>diamonds){
                    sticks-=2;
                    diamonds--;
                    emeralds++;
                }else{
                    sticks--;
                    diamonds -=2;
                    emeralds++;
                }
            }else{
                if(sticks % 3 == 0){
                    emeralds += sticks / 3 * 2;
                }else if(sticks % 3 == 2){
                    emeralds += sticks / 3 * 2 + 1;
                }else if(sticks % 3 == 1){
                    emeralds += (sticks - 1) / 3 * 2;
                }
                break;
            }
        }
        return emeralds;
       }
}