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(NULL);
  int i, n;
  cin >> n;
  while (n--) {
    long long int f, g, a, b;
    cin >> f >> g;
    if (min(f, g) == 0) {
      cout << "0" << endl;
      continue;
    }
    a = min(f, g);
    b = max(f, g);
    long long int c = b / a, ans = 0;
    if (c >= 2) {
      cout << a << endl;
      continue;
    } else {
      long long int d = b - a;
      ans = d;
      b = b - d - d;
      a = a - d;
      int z = a / 3;
      a = a - (z * 3);
      b = b - (z * 3);
      ans = ans + (z * 2);
      if (a == 2) {
        ans = ans + 1;
      }
      cout << ans << endl;
    }
  }
  return 0;
}
