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.
tc = int(input());
for _ in range(tc):
  sticks,diamonds = map(int,input().split());
  if sticks >= 2*diamonds:
    print(diamonds);
  elif diamonds >= 2*sticks:
    print(sticks);
  else:
    diff = abs(sticks-diamonds);
    bigger = max(sticks,diamonds); smaller = min(sticks,diamonds);
    emeralds = diff;
    #print(emeralds);
    bigger -= diff * 2;
    smaller -= diff;
    pairs = bigger // 3 * 2;
    emeralds += pairs;
    smaller -= pairs // 2 * 3;
    bigger -= pairs // 2 * 3;
    if (bigger >= 1 and smaller >= 1) and ((bigger >= 2*smaller) or (smaller >= 2*bigger) or (bigger >= smaller + 1 or smaller >= bigger + 1) or (bigger >= 2 and smaller <= 2)):
      emeralds += 1;
    #  print("nice");
    print(emeralds);