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 Solution {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int t=s.nextInt();
		while(t-->0) {
	    long a= s.nextLong();
	    long b= s.nextLong();
	    if(a==0||b==0) {
	    	System.out.println(0);
	    	continue;
	    }
	    long lar = Math.max(a, b);
	    long smal = Math.min(a, b);
	    long count =0;
	    if(smal>lar/2) {
	    	count = lar/2;
	    	count -=1;
	    	smal=smal-count;
	    	count+=smal/2;
	    	System.out.println(count);
	    }
	    else {
	    	System.out.println(lar/2);
	    }
			
			
			
			
		}
	}
	
}
