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;

public class ShovelsSword {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(reader.readLine());
        while (t-- > 0) {
            String s = reader.readLine();
            String[] arr = s.split(" ");
            long a = Long.parseLong(arr[0]);
            long b = Long.parseLong(arr[1]);
            if (a == b) {
                System.out.println(a / 2);
            } else if (a == 0 || b == 0) {
                System.out.println(0);
            } else if (a > b) {
                solve(a, b);
            } else {
                solve(b, a);
            }
        }
    }

    private static void solve(long a, long b) {
        long arem = 0, brem = 0;
        if (b % 2 != 0) {
            brem = 1;
            b--;
        }
        arem = a - b;
        long ans = b / 2;
        brem += b - ans;
        if (arem > brem) {
            ans += arem / 2;
        } else {
            ans += brem / 2;
        }
        System.out.println(ans);
    }
}
