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 scanner=new Scanner(System.in);
		int n=scanner.nextInt();
		for(int i=0;i<n;i++) {
			int gz=0,zs=0,max=0;
			gz=scanner.nextInt();
			zs=scanner.nextInt();
				if(gz>=2*zs) {
					max=zs;
					
				}
				else {
				if(2*gz<=zs) {		
					max=gz;
				}
				else
				max=(gz+zs)/3;
				}
				System.out.println(max);
				}
	}
}
