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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Shovel_Swords {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next(){
            while(st==null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt(){
            return Integer.parseInt(next());
        }
        long nextLong(){
            return Long.parseLong(next());
        }
        String nextLine(){
            String str = "";
            try
            {
                str = br.readLine();
            }catch (IOException e){
                e.printStackTrace();
            }
            return str;
        }
        double nextDouble(){
            return Double.parseDouble(next());
        }
    }
    public static void main(String[] args) {
        FastReader in = new FastReader();
        int t = in.nextInt();
        while(t-- > 0){
            long a = in.nextLong();
            long b = in.nextLong();
            long min = Math.min(a,b);
            long max = Math.max(a,b);
            if(min == 0 || max == 0){
                System.out.println(0);
            } else if(min * 2 <= max){
                System.out.println(min);
            }else{
                long ans = 0;
                if(min != max){
                    long x = max - min;
                    ans += x;
                    max -= 2*x;
                    min -= x;
                }
                ans += (min/3)*2;
                if(min % 3 == 2){
                    ans += 1;
                }
                System.out.println(ans);
            }
        }
    }
}
