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.
def f(a,b):
	if b < a:
		return f(b,a)
	x = min(a, b/2, b - a)
	if x == 0:
		t = min(a,b)/3 
		a -= t * 3
		b -= t * 3
		return 2 * t + (1 if ((a and b >=2) or (b and a >= 2)) else 0) 
	else:
		return x + f(a- x, b - 2 * x)
for _ in range(int(raw_input())):
	a,b = map(int, raw_input().split(' '))
	print f(a,b)#,m, [map(int, raw_input().split(' ')) for _ in range(m)])