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 long long int MOD = 1e9 + 7;
const long long int MAXN = 1e5 + 5;
long long int fastexpo(long long int b, long long int exp) {
  if (exp == 0) return 1;
  if (exp == 1) return b;
  long long int ans = (fastexpo(b, exp / 2) % MOD);
  ans *= ans;
  ans %= MOD;
  if (exp % 2 == 1) {
    ans *= b;
  }
  ans %= MOD;
  return ans;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int t;
  cin >> t;
  while (t--) {
    long long int n, m;
    cin >> n >> m;
    if (min(n, m) == 0) {
      cout << 0 << endl;
      continue;
    }
    if (min(n, m) * 2 < max(n, m)) {
      cout << min(n, m) << endl;
    } else {
      cout << (n + m) / 3 << endl;
    }
  }
  return 0;
}
