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.Arrays;
import java.util.Collections;
import java.util.Scanner;
import java.util.Vector;
public class NewClass {
	public static void main(String[] args) {
		Scanner ob=new Scanner(System.in);
		int t=ob.nextInt();
		out:for(int T=1;T<=t;T++)
		{
		int a=ob.nextInt();
		int b=ob.nextInt();
		if(a==0||b==0){System.out.println(0);continue out;}
		if(a>=(2*b)){System.out.println(b);continue out;}
		if(b>=(2*a)){System.out.println(a);continue out;}
		System.out.println((a+b)/3);
		}		
	}
}
