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 in=new Scanner(System.in);
		int t=in.nextInt();
		while(t-->0){
			int a= in.nextInt();
			int b=in.nextInt();
			int k=(Math.min(a,b))/3;
			int d=Math.min(a,b)-(3*k);
			int e=Math.max(a,b)-(3*k);
			if(Math.max(a,b)>2*Math.min(a,b))
			System.out.println(Math.min(a,b));
			else if(d==1 && e>=2)
			System.out.println(1+2*k);
			else if(d==2 && e>=4)
			System.out.println(2*(1+k));
			else if(d==1 && e==1)
			System.out.println(2*k);
			else if(d==2 && e<=3)
			System.out.println(1+2*k);
			else if(d==0)
			System.out.println(2*k);
			
		}
			
	}
}