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;
using ll = long long;
int ans = 0;
bool verbose = 0;
template <class T>
void print_vector(T a, string name) {
  if (!verbose) return;
  cout << name + ": ";
  for (auto i = a.begin(); i < a.end(); i++) cout << *i << " ";
  cout << endl;
}
template <class T>
void print_array(T *a, int n, string name) {
  if (!verbose) return;
  cout << name + ": ";
  for (auto i = 0; i < n; i++) cout << a[i] << " ";
  cout << endl;
}
template <class T>
void print_var(T a, string name) {
  if (!verbose) return;
  cout << name + ": " << a << endl;
}
template <class T>
void print(T a) {
  cout << a << endl;
}
void solve() {
  ll a, b;
  cin >> a >> b;
  ll nums = (a + b) / 3;
  ll min_ = min(a, b);
  print(min(nums, min_));
}
int main() {
  int num;
  cin >> num;
  while (num--) solve();
  return 0;
}
