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;
long long gcd(long long a, long long b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
ll mypower(ll x, ll n, ll c) {
  ll ans = 1;
  if (n == 0) return 1;
  ll temp = mypower(x, n / 2, c) % c;
  if (n % 2)
    return (n < 0) ? (1 / x) * temp * temp % c : ((x * temp) % c) * temp % c;
  else
    return temp * temp % c;
}
bool codejam = 0;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ll t;
  cin >> t;
  ll tc = 1;
  while (t--) {
    if (codejam) {
      cout << "Case #" << tc++ << ": ";
    }
    ll s, d;
    cin >> s >> d;
    if (s == 0 || d == 0) {
      cout << 0 << "\n";
      continue;
    }
    long long temps = s;
    temps /= 2;
    long long ans = min(temps, d) + (max(d, temps) - min(d, temps)) / 3;
    long long tempd = d;
    tempd /= 2;
    ans = max(ans, min(tempd, s) + (max(s, tempd) - min(s, tempd)) / 3);
    cout << ans << "\n";
  }
  return 0;
}
