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 maxn = 2e5 + 5;
int x[maxn], s[maxn], w[maxn];
int n, m;
bool ok(int x, int y) { return x >= 0 && x < n && y >= 0 && y < m; }
void run() {
  cin >> n >> m;
  if (n > m) swap(n, m);
  int ans = 0;
  int nn = n;
  int mm = m;
  if (m >= 2 * n) {
    cout << n << '\n';
    return;
  }
  int temp = m - n;
  m -= 2 * temp;
  ans += temp;
  n = m;
  ans += m / 3 * 2;
  cout << ans << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  int t;
  cout << fixed << setprecision(20);
  for (cin >> t; t--;) {
    run();
  }
}
