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 getans(long long a, long long b) {
  long long x = min(a, b / 2);
  a -= x;
  b -= 2 * x;
  x += min(b, a / 2);
  return x;
}
void solve() {
  long long a, b;
  cin >> a >> b;
  if (a < b) swap(a, b);
  if (a >= 2 * b) {
    cout << min(a / 2, b) << endl;
    return;
  }
  long long y = (a - 2 * b) / (-3);
  long long x = (a - y) / 2;
  cout << x + y << endl;
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}
