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;
const int MOD = 1e9 + 7;
const double EPS = 1e-6;
const string alpha = "abcdefghijklmnopqrstuvwxyz";
const int INF = 1e9;
const int maxV = 1e6;
void test_case() {
  int a, b;
  cin >> a >> b;
  if (a >= 2 * b || b >= 2 * a) {
    cout << min(a, b) << endl;
    return;
  }
  cout << (a + b) / 3 << endl;
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    test_case();
  }
}
