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;

public class Solution {
  private static int calculateEmeralds(int a, int b) {
    // if a > b, call with reverse arguments
    if (a > b) {
      return calculateEmeralds(b, a);
    }
    if (a < 2 && b < 2)
      return 0;
    // Now b >= a
    if (b >= 2 * a) {// b is twice a so max a can be used
      return a;
    } else if (b < 2 * a) {
      int em = b / 2;
      int rest_b = b - 2 * em;
      int rest_a = a - em;
      return em + calculateEmeralds(rest_a, rest_b);
    }
    return -9999;
  }

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