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;
long long fx[4] = {1, -1, 0, 0};
long long fy[4] = {0, 0, 1, -1};
bool rs(long long a, long long b) { return (a > b); }
int main() {
  long long t;
  cin >> t;
  while (t--) {
    long long a, b;
    cin >> a >> b;
    if (a == 0 || b == 0)
      cout << "0" << endl;
    else {
      if (a == b)
        cout << (a / 2) << endl;
      else if (a > b) {
        long long d = a / b;
        if (d == 1) {
          long long k = round(a + b + 1) / 3;
          cout << k << endl;
        } else if (d > 1) {
          cout << b << endl;
        }
      } else if (a < b) {
        long long dd = b / a;
        if (dd == 1) {
          cout << (a + b + 1) / 3 << endl;
        } else if (dd > 1) {
          cout << a << endl;
        }
      }
    }
  }
  return 0;
}
