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.
query = int(input())
#corner_case = [[0,0],[0,1],[1,0],[1,1]]
for i in range(query) :
	a,b = list(map(int,input().split()))
	#n = 0
	if a >=1 and b >=1 and [a,b] != [1,1]:
		x = int(max((2*a-b)/3,0))
		y = int(max((2*b-a)/3,0))
		if x < y :
			y = int(min(a-2*x,(b-x)/2))
		else :
			x = int(min(b-2*y,(a-y)/2))
		print(x+y)
	else :
		print(0)

	"""
	while a >=1 and b >=1 and [a,b] != [1,1] :
		if a>b :
			a -= 2
			b -= 1
		else :
			a-= 1
			b -= 2
		n += 1
	print(n)
	"""