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;
int main() {
  int t;
  cin >> t;
  while (t--) {
    long long s, d;
    cin >> s >> d;
    if (s == 0 || d == 0 || s / d >= 2 || d / s >= 2) {
      cout << min(s, d) << endl;
    } else {
      long long int count = max(s, d) - min(s, d);
      if (s > d) {
        s = s - 2 * count;
        d = d - count;
      } else {
        d = d - 2 * count;
        s = s - count;
      }
      count = count;
      long long ans = 0;
      if (s % 3 == 0) {
        ans = (s / 3) * 2 + count;
      } else {
        ans = (s / 3) * 2;
        s = s - 3 * (s / 3);
        d = s;
        if (d > 1 && s >= 1 || d >= 1 && s > 1) {
          ans = ans + 1;
        }
        ans = ans + count;
      }
      cout << ans << endl;
    }
  }
  return 0;
}
