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.Scanner;

//https://codeforces.com/contest/1366/problem/A
public class ShovelsAndSwords {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int testCases = sc.nextInt();
        for (int i = 0; i < testCases; i++) {
            int sticks = sc.nextInt();
            int diamonds = sc.nextInt();
            System.out.println(noOfEmerals(sticks , diamonds));
        }
    }

    private static int noOfEmerals(int sticks, int diamonds) {
        if( 0 == sticks || 0 == diamonds){
            return 0;
        } else if((2*sticks)< diamonds){
            return sticks;
        } else if((2*diamonds)< sticks){
            return diamonds;
        } else if((2*diamonds) == sticks){
            return diamonds;
        } else if((2*sticks)== diamonds){
            return sticks;
        } else {
            return (sticks + diamonds)/3;
        }
    }
}