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) 
	
	{
		Scanner scan = new Scanner(System.in);
		int t = scan.nextInt();
		while(t-->0)
		{
			long X = scan.nextInt(), Y= scan.nextInt();
			long a = Math.max(X, Y), b = Math.min(X, Y);
			if(a==b)System.out.println(Math.max((a-1-(a-1)/3),0));
			else if(a>=2*b)System.out.println(b);
			else System.out.println(((2*b-a)-1-((2*b-a)-1)/3)+(a-b));
		}
	}
	

}
