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 square
{
 
    public static void main(String ar[])
    {
        Scanner sc=new Scanner(System.in);
       int t=sc.nextInt();
       for(int k=1;k<=t;k++)
       {
           
int a=sc.nextInt(),b=sc.nextInt();
if(a==0 || b==0){System.out.println("0");continue;}
int em=0;
if(a>b)
{
    int temp=a;a=b;b=temp;
}
if(2*a<=b) em=a;
else{
    em=b/2;b=b%2;a=a-em;if(a>=2 && b>=1)em++;
}
System.out.println(em);
  }
    }
}