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.
//package codeforces.div2;

import java.util.Scanner;

public class ShovelsAndSwords {

    static public void print(long a , long b) {


        long total = 0;
        if(2*b<=a) {
            total = b;
        } else {
            if(2*a<=b) {
                total = a;
            } else {
                total = (a + b)/3;
            }
        }
        System.out.println(total);
    }
    public static void main(String []args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        while ( n > 0) {
            long p = sc.nextLong();
            long y = sc.nextLong();
            print(p, y);
            n--;

        }
    }
}
