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.
t = int(input())
ans=[0]*t

for i in range(t):
  a,b=map(int,input().split())
  if a>b*2:
    ans[i]=b
  elif a>b:
    ans[i]=a-b+((2*b-a)//3)*2+((2*b-a)%3)//2
  elif a==b:
    ans[i]=((2*b-a)//3)*2+((2*b-a)%3)//2
  elif b>a*2:
    ans[i]=a
  else:
    ans[i]=-a+b+((-b+2*a)//3)*2+((-b+2*a)%3)//2

for i in range(t):
  print(int(ans[i]))