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() {
  int n, m, k = 0;
  cin.tie(0);
  cout.tie(0);
  int T;
  cin >> T;
  while (T--) {
    cin >> n >> m;
    if (n == 0 || m == 0) {
      cout << 0 << "\n";
      continue;
    }
    if (n == m) {
      cout << n / 2 << "\n";
      continue;
    }
    if (n > m) {
      n /= 2;
      m -= n;
      k += n;
      if (m > 2) {
        m /= 2;
        n -= m;
        k += m;
      }
      cout << k << "\n";
      k = 0;
      continue;
    } else {
      m /= 2;
      n -= m;
      k += m;
      if (n > 2) {
        n /= 2;
        m -= n;
        k += n;
      }
    }
    cout << k << "\n";
    k = 0;
  }
  return 0;
}
