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 int find_ans() {
  long long int i, j, k, a, b, c, d, p = 0;
  cin >> a;
  cin >> b;
  p = (a > b) ? (b < (a + b) / 3 ? b : (a + b) / 3)
              : (a < (a + b) / 3 ? a : (a + b) / 3);
  return p;
}
int32_t main() {
  long long int t, g, i;
  vector<long long int> ans;
  cin >> t;
  for (g = 0; g < t; g++) ans.push_back(find_ans());
  for (g = 0; g < t; g++) cout << ans[g] << "\n";
  return 0;
}
