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;
void solve() {
  long long int a, b;
  cin >> a >> b;
  long long int ans = 0;
  if (a < b) {
    long long int temp = a;
    a = b;
    b = temp;
  }
  long long int reduce = min(b, min(a - b, a / 2));
  ans += reduce;
  a -= 2 * reduce;
  b -= reduce;
  if (a == b) {
    ans += 2 * (a / 3);
    if (a % 3 == 2) {
      ans++;
    }
  }
  cout << ans << "\n";
}
int32_t main() {
  long long int t = 1;
  scanf("%lld", &t);
  for (long long int i = 0; i < t; i++) {
    solve();
  }
  cerr << "\n"
       << "Time elapsed : " << clock() * 1000.0 / CLOCKS_PER_SEC << " ms"
       << '\n';
  return 0;
}
