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;
bool cmp(const pair<int, int>& a, const pair<int, int>& b) {
  return a.first < b.first;
}
void solve() {
  long long n, m, i = 0, count = 0;
  cin >> n >> m;
  if (!n || !m || (n == 1 && m == 1)) {
    cout << 0 << '\n';
  } else {
    if (abs(n - m) == 1 || 0 || 2) {
      cout << (n + m) / 3 << '\n';
    } else {
      long long a = max(n, m);
      long long b = min(n, m);
      long long k = min(a / 2, b);
      a = a - 2 * k;
      b = b - k;
      if (a) {
        if (b > 1) count++;
      }
      cout << k + count << '\n';
    }
  }
  return;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}
