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 = 1e5 + 15;
const int mod = 998244353;
const int inf = 0x3f3f3f3f;
int n, m;
int a, b;
int calc(int x) {
  if (x < 0) return 0;
  int ans = x;
  int aa = a - 2 * x;
  int bb = b - x;
  if (aa < 0 || bb < 0) return 0;
  ans += min(aa, bb / 2);
  return ans;
}
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &a, &b);
    int x = max(0, (2 * a - b) / 3);
    x = min(x, b);
    int ans = 0;
    ans = calc(x);
    ans = max(ans, calc(x - 1));
    ans = max(ans, calc(x + 1));
    printf("%d\n", ans);
  }
  return 0;
}
