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.*;
import java.io.*;

public class A{
	private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	private static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	
	public static void main (String[] args) throws java.lang.Exception
	{
		int t = Integer.parseInt(br.readLine());
		while(t-- > 0){
            StringTokenizer st = new StringTokenizer(br.readLine());
		    int a = Integer.parseInt(st.nextToken());
            int b = Integer.parseInt(st.nextToken());
            if(a==b){
                a -= 1;
            }
            if(a<=b){
                if(2*a>b){
                    int count = b/2;
                    a = a - b/2;
                    int q = a/2;
                    count += q;
                    bw.write(count + " ");
                    bw.newLine();
                }else{
                    bw.write(a + " ");
                    bw.newLine();
                }
            }else if(b<a){
                if(2*b>a){
                    int count = a/2;
                    b = b - a/2;
                    int q = b/2;
                    count += q;
                    bw.write(count + " ");
                    bw.newLine();
                }else{
                    bw.write(b + " ");
                    bw.newLine();
                }
            }
		}
		bw.flush();
	}
}
