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.
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import java.util.*;
import java.io.*;
public class Main{
     public static void main(String []args) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        PrintWriter out = new PrintWriter(System.out);
        int trials = Integer.parseInt(st.nextToken());
        for(int trial = 0; trial < trials; trial++){
            st = new StringTokenizer(br.readLine());
            int a = Integer.parseInt(st.nextToken());
            int b = Integer.parseInt(st.nextToken());
            if(b >= 2*a)
                out.println(a);
            else if(a >= 2*b)
                out.println(b);
            else if(b >= a){
                int c = 2*a-b;
                int ans = b-a + (c/3)*2;
                if(c%3 == 2)
                    ans++;
                out.println(ans);
            }
            else{
                int c = 2*b-a;
                int ans = a-b + (c/3)*2;
                if(c%3 == 2)
                    ans++;
                out.println(ans);
            }
        }
        out.close();
     }
}