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 Practise {
    static Scanner in = new Scanner(System.in);

    static int[] array(int n) {
        int[] a = new int[n];
        for(int i = 0; i < n; i++) a[i] = in.nextInt();
        return a;
    }

    static int[][] matrix(int r, int c) {
        int[][] a = new int[r][c];
        for(int i = 0; i < r; i++) {
            for(int j = 0; j < c; j++) {
                a[i][j] = in.nextInt();
            }
        }
        return a;
    }

    static public void solve() {

        int s = in.nextInt();
        int d = in.nextInt();
        int e = (s + d) / 3;
        if(e > d) e = d;
        if(e > s) e = s;

        System.out.println(e);


    }

    public static void main(String[] args) {
       int t = in.nextInt();
       while(t-- > 0) solve();
    }

}



