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.*;
import java.io.*;

public class Codeforces_1366_A {
	static Scanner sc;
	static final long MOD = 1000000007;

	public static void main(String[] args) throws FileNotFoundException {
		boolean submit = true;
		if (submit) {
			sc = new Scanner(System.in);
			System.out.println();
		} else {
			File f = new File("src/input.txt");
			sc = new Scanner(f);
		}

		int T = sc.nextInt();
		for (int t = 0; t < T; t++) {

			solve();
		}

		sc.close();
	}

	static void solve() {
		// Solution Here
		int at = sc.nextInt();
		int bt = sc.nextInt();
		int a = Math.min(at, bt);
		int b = Math.max(at, bt);
		if (a == 0 || b == 0) {
			System.out.println(0);
			return;
		}

		if (a <= (b / 2)) {
			System.out.println(a);
			return;
		}
		if (b <= (a / 2)) {
			System.out.println(b);
			return;
		}
		
		long sum=(long)a +(long)b;
		System.out.println(sum/3);

	}

}
