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.
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int t;
  cin >> t;
  while (t--) {
    long long int a, b, p, q, r, s, ans1, ans = 0;
    cin >> a >> b;
    if (b >= 2 * a)
      cout << a << '\n';
    else if (a >= 2 * b)
      cout << b << '\n';
    else {
      p = a / 3;
      q = b / 3;
      r = p * 3;
      s = q * 3;
      ans1 = min(r, s);
      ans += 2 * (ans1 / 3);
      a = a - ans1;
      b = b - ans1;
      if (b >= 2 * a)
        ans = ans + a;
      else if (a >= 2 * b)
        ans = ans + b;
      cout << ans << '\n';
    }
  }
}
