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 _0842ShovelsandSwords {

	public static void main(String[] args) {
		
		Scanner  sc = new Scanner(System.in);
		int t=sc.nextInt();
		while(t>0) {
				int a=sc.nextInt();
				int b=sc.nextInt();
//				int min=0;
//				int temp=0;
//				temp=Math.min(a/4,b/2);
//				a-=temp;
//				b-=temp;
//				min=temp;
//				temp=Math.min(a/2, b/4);
			//	min+=temp;
				System.out.println(Math.min(a, Math.min(b,(a+b)*1L/3)));
			t--;
		}
	}

}
