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;
const int mod = 1e9 + 7;
const int N = 100010;
void go() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
long long modExp(long long a, long long b, long long c) {
  long long ans = 1;
  a = a % c;
  if (a == 0) return 0;
  while (b > 0) {
    if (b & 1) ans = (ans * a) % c;
    b = b >> 1;
    a = (a * a) % c;
  }
  return ans;
}
void solve() {
  long long d, s, ans = 0;
  cin >> s >> d;
  cout << min(d, min(s, (d + s) / 3)) << "\n";
}
int32_t main() {
  go();
  int t;
  cin >> t;
  while (t--) solve();
  return 0;
}
