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;
using ld = long double;
using P = pair<int, int>;
using PLL = pair<ll, ll>;
template <typename T>
void view(T e) {
  std::cout << e << std::endl;
}
template <typename T>
void view(const std::vector<T> &v) {
  for (const auto &e : v) {
    std::cout << e << " ";
  }
  std::cout << std::endl;
}
template <typename T>
void view(const std::vector<std::vector<T>> &vv) {
  for (const auto &v : vv) {
    view(v);
  }
}
template <typename T>
inline istream &operator>>(istream &i, vector<T> &v) {
  for (int j = 0; j < (int)((int)v.size()); j++) i >> v[j];
  return i;
}
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
T gcd(T a, T b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
template <class T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
template <class T = int>
using V = vector<T>;
template <class T = int>
using VV = vector<V<T>>;
bool isIn(int i, int j, int h, int w) {
  return i >= 0 && i < h && j >= 0 && j < w;
}
void Yes() { cout << "Yes" << endl; }
void No() { cout << "No" << endl; }
void YES() { cout << "YES" << endl; }
void NO() { cout << "NO" << endl; }
void err() { cout << -1 << endl; }
const int MOD = 1000000007;
const int INF = 1e9;
int dx[4] = {1, -1, 0, 0};
int dy[4] = {0, 0, 1, -1};
int ddx[8] = {1, 1, 1, -1, -1, -1, 0, 0};
int ddy[8] = {0, 1, -1, 0, 1, -1, 1, -1};
void solve() {
  int a, b;
  cin >> a >> b;
  if (a < b) swap(a, b);
  if (b * 2 <= a)
    cout << b << endl;
  else
    cout << (a + b) / 3 << endl;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int t;
  cin >> t;
  while (t--) solve();
}
