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() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  while (t--) {
    long long int a, b;
    cin >> a >> b;
    if (a > 2 * b) {
      cout << b << "\n";
    } else if (b > 2 * a) {
      cout << a << "\n";
    } else if (a == b) {
      if (a & 1) {
        cout << a / 2 + 1 << "\n";
      } else {
        cout << a / 2 << "\n";
      }
    } else {
      long long int em = 0;
      if (a > b) {
        long long int rem = b / 2;
        a -= 2 * rem;
        b -= rem;
        em += rem;
        rem = a / 2;
        if (rem >= a) {
          em += a;
        } else {
          em += rem;
        }
      } else {
        long long int rem = a / 2;
        em += rem;
        b -= 2 * rem;
        a -= rem;
        rem = a / 2;
        if (rem >= b) {
          em += b;
        } else {
          em += rem;
        }
      }
      cout << em << "\n";
    }
  }
}
