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 t;
  cin >> t;
  int* a = new int[t];
  int* b = new int[t];
  for (int i = 0; i < t; ++i) {
    cin >> a[i] >> b[i];
  }
  int temp, maxEmeralds;
  int n = 0;
  for (int i = 0; i < t; ++i) {
    n = 0;
    maxEmeralds = 0;
    n = floor((a[i] - b[i] / 2.0) * 2.0 / 3.0);
    n = min(n, a[i] / 2);
    n = min(n, b[i]);
    if (n >= 0) {
      maxEmeralds = floor(b[i] / 2.0 + n / 2.0);
    }
    n = ceil((a[i] - b[i] / 2.0) * 2.0 / 3.0);
    n = max(n, 0);
    if (n <= b[i] && n <= a[i] / 2) {
      temp = floor(a[i] - n);
      if (temp > maxEmeralds) maxEmeralds = temp;
    }
    cout << maxEmeralds << endl;
  }
  delete[] a;
  delete[] b;
  return 0;
}
