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;
long long int Ceil(long long int a, long long int b) {
  return a / b + (a % b != 0);
}
long long int fastModExp(long long int a, long long int b) {
  long long int res = 1;
  while (b > 0) {
    if (b & 1) res = (res * a) % 1000000007;
    a = (a * a) % 1000000007;
    b = b >> 1;
  }
  return res;
}
long long int Logn(long long int n, long long int r) {
  return (n > r - 1) ? 1 + Logn(n / r, r) : 0;
}
map<long long int, long long int> mpx, mpx2;
int main() {
  long long int t;
  cin >> t;
  while (t--) {
    long long int a, b, x, y;
    cin >> a >> b;
    long long int r = 2 * a - b;
    if (a == 0 || b == 0) {
      cout << 0 << endl;
      continue;
    }
    x = r / 3;
    if (r > 0) {
      y = (b - x) / 2;
      cout << x + y << endl;
    } else {
      cout << a << endl;
    }
  }
  return 0;
}
