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 int a, b, ans, k, x, y;
    cin >> a >> b;
    if (a == 0 || b == 0) {
      cout << "0" << endl;
      continue;
    }
    x = a / 3;
    y = b / 3;
    k = min(x, y);
    k *= 2;
    if ((a % 3 != 1 || b % 3 != 1) && (a % 3 != 0 && b % 3 != 0)) k++;
    ans = -1;
    ans = max(ans, k);
    if (a < b) swap(a, b);
    if (a % 2 == 1) {
      if (b >= 2 + a / 2) {
        k = a / 2 + 1;
      } else {
        k = min(a / 2, b);
      }
    } else {
      k = min(a / 2, b);
    }
    ans = max(ans, k);
    cout << ans << endl;
  }
}
