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;
istream& inp = cin;
template <typename T>
T divup(T a, T b) {
  assert(b > 0);
  if (a < 0) return -((-a) / b);
  if ((a % b) == 0) return a / b;
  return 1 + a / b;
}
int64_t tryy(int64_t a1, int64_t b1) {
  int64_t m = max(int64_t(0), divup(2 * a1 - b1, int64_t(3)));
  int64_t l = a1 - 2 * m;
  if (l < 0) return 0;
  return m + l;
}
int32_t main() {
  int64_t ntests;
  assert(inp);
  inp.tie(NULL);
  inp >> ntests;
  for (int64_t test = 0; test < ntests; ++test) {
    int64_t a, b;
    inp >> a >> b;
    if (min(a, b) == 0)
      cout << 0 << "\n";
    else {
      int64_t ans = tryy(a, b);
      ans = max(ans, tryy(a - 1, b));
      ans = max(ans, tryy(b, a));
      ans = max(ans, tryy(b - 1, a));
      cout << ans << endl;
    }
  }
  return 0;
}
