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 ShowelSword {

	public static void main(String[] args) {
		Scanner s=new Scanner(System.in);
		int t= s.nextInt();
		
		while(t-->0) {
			long a= s.nextLong();
			long b= s.nextLong();
			
			if(a>b) {
				long temp= a;
				b=a;
				a= temp;
			}
			
			if(a==0 || b==0) {
				System.out.println(0);
				continue;
			}
			
			long ans= 0;
			
			if(b >= 2*a)
				ans = a;
			else if(b==a) 
				ans= (((b/3)*2) + ((b%3 == 2) ? 1 : 0));
			else
				ans= b/2;
			
			System.out.println(ans);
					
			
		}
	}

}
