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 pow(long long c, long long d) { return d == 0 ?: c * pow(c, d - 1); }
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
long long lcm(long long a, long long b) { return ((a * b) / gcd(a, b)); }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t;
  cin >> t;
  while (t--) {
    long long a, b;
    cin >> a >> b;
    long long mx = max(a, b);
    long long mn = min(a, b);
    if (mn * 2 <= mx) {
      cout << mn << endl;
      continue;
    }
    long long ans = (mx - mn);
    mn -= ans;
    mx -= (ans * 2);
    long long x = min(mn / 3, mx / 3);
    mn -= x * 3;
    mx -= x * 3;
    ans += x * 2;
    if (mn == 1) {
      if (mx >= 2) ans += 1;
    }
    if (mn == 2) {
      if (mx >= 4)
        ans += 2;
      else
        ans += 1;
    }
    cout << ans << endl;
  }
  return 0;
}
