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.*;
public class Main
{
	public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int T= s.nextInt();
        while(T-->0){
            long n = s.nextLong();
            long m= s.nextLong();
            double x= (2*m-n)/3;
            double y=(2*n-m)/3;
            // System.out.println(x+" "+y);
            if(x>=0&& y>=0){
                System.out.println((long)(x+y));
            }
            else if(x<0&&y>=0){
                System.out.println((long)m);
            }else{
                System.out.println(0);
            }
        }
	}
}
