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() {
  long long t;
  cin >> t;
  while (t--) {
    long long a, b;
    cin >> a >> b;
    long long c = 0;
    while (1) {
      if ((a <= 1) || (b <= 1)) {
        break;
      }
      if (a > b) {
        long long k = b, k1 = 1;
        while (k > 0) {
          k -= k1;
          k1 *= 2;
        }
        b -= k1 / 4;
        a -= k1 / 2;
        c += k1 / 4;
      } else if (a <= b) {
        long long k = a, k1 = 1;
        while (k > 0) {
          k -= k1;
          k1 *= 2;
        }
        a -= k1 / 4;
        b -= k1 / 2;
        c += k1 / 4;
      }
    }
    if (((a >= 2) && (b == 1)) || ((a == 1) && (b >= 2))) {
      c++;
    }
    cout << c << endl;
  }
  return 0;
}
