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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Problem89A {
	public static void main(String[] args) throws Exception {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter writer = new PrintWriter(System.out);

		int t = Integer.parseInt(reader.readLine());
		for (int tt = 0; tt < t; tt++) {
			StringTokenizer tokenizer = new StringTokenizer(reader.readLine());
			int n = Integer.parseInt(tokenizer.nextToken());
			int m = Integer.parseInt(tokenizer.nextToken());

			int max = Math.max(n, m);
			int min = Math.min(n, m);
			int diff = max - min;
			if (diff <= min) {
				int total = diff;
				int leftover = min - diff;
				if (leftover >= 3) {
					total += 2 * (leftover / 3);
					leftover = leftover % 3;
				}
				if (leftover == 2) {
					total++;
				}
				writer.println(total);
			} else {
				writer.println(min);
			}



		}

		reader.close();
		writer.close();
	}
}
