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;
int GCD(int x, int y) {
  if (y == 0) return x;
  return GCD(y, x % y);
}
bool isPalindrome(string s) {
  int l = 0;
  int h = s.size() - 1;
  while (h > l) {
    if (s[l++] != s[h--]) {
      return false;
    }
  }
  return true;
}
long long int pairs(long long int n) { return (n * (n - 1)) / 2; }
bool isSquare(long long int n) {
  int sq_root = sqrt(n);
  if (sq_root * sq_root == n) {
    return true;
  }
  return false;
}
bool isPrime(long long int n) {
  for (long long int i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    long long int a, b;
    cin >> a >> b;
    if (a == 0 || b == 0) {
      cout << 0 << endl;
    } else {
      long long int t = (a + b) / 3;
      cout << t << endl;
    }
  }
}
