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;
const int Maxn = 1e6 + 1;
const int Mod = 1e9 + 7;
const long long int MOD = 1000000007LL;
const long long int MAX = 100010LL;
template <typename T>
T gcd(T a, T b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
template <typename T>
T power(T x, T y, long long int m = MOD) {
  T ans = 1;
  x %= m;
  while (y > 0) {
    if (y & 1ll) ans = (ans * x) % m;
    y >>= 1ll;
    x = (x * x) % m;
  }
  return ans % m;
}
template <typename T, typename T1>
T mod(T x, T1 p) {
  x %= p;
  if (x < 0) x += p;
  return x;
}
int inv[Maxn], ifact[Maxn], fact[Maxn];
template <typename T>
T inverse(T x, T p) {
  x = mod(x, p);
  if (x == 1) return x;
  return mod((1LL * (-p / x) * (inv[p % x] % p)), p);
}
long long int NcR(long long int n, long long int r) {
  int ret = (1LL * ifact[n - r] * ifact[r]) % Mod;
  ret = (1LL * ret * fact[n]) % Mod;
  return ret;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  for (int z = 0; z < t; z++) {
    long long int a, b;
    cin >> a >> b;
    if (a > b) swap(a, b);
    if (a == 0 || b == 0) {
      cout << 0 << endl;
      continue;
    }
    long long int ans = 0;
    long long int dif = b - a;
    if (dif < a) {
      ans += dif;
      a -= dif;
      ans += (a / 3) * 2;
      a = a % 3;
      if (a >= 2) ans++;
    } else {
      ans += a;
    }
    cout << ans << endl;
  }
}
