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;
bool isprime(long long int x) {
  for (long long int i = 2; i <= sqrt(x); i++) {
    if (x % i == 0) return false;
  }
  return true;
}
bool simcomp(long long int a, long long int b) { return (a > b); }
void showvector(vector<long long int> v) {
  for (long long int x : v) cout << x << " ";
  cout << "\n";
}
bool iseven(long long int x) { return !(x % 2); }
bool isodd(long long int x) { return (x % 2); }
void showset(set<char> s) {
  for (char x : s) cout << x;
  cout << "\n";
}
bool comp(pair<long long int, long long int> a,
          pair<long long int, long long int> b) {
  return (a.first > b.first);
}
void fun() {
  long long int a, b;
  cin >> a >> b;
  long long int x = max(a, b);
  long long int y = min(a, b);
  long long int cnt = x / 2;
  long long int left = y - cnt;
  if (left < 0) {
    cout << y << "\n";
    return;
  } else {
    if (x % 2 == 1) {
      if (left >= 2) {
        cnt++;
        left -= 2;
      }
    }
    left += 1;
    while (left >= 4) {
      cnt += left / 4;
      long long int rem = left % 4;
      left = left / 4 + rem;
    }
    cout << cnt << "\n";
  }
}
void vfun() {
  long long int n, k;
  cin >> n;
  vector<long long int> v(n);
  for (long long int i = 0; i < n; i++) cin >> v[i];
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int test = 1;
  cin >> test;
  while (test--) {
    fun();
  }
}
