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.
# f = open('test.py')
# def input():
# 	return f.readline()


def read_list():
	return list(map(int,input().split(' ')))
N = int(input())
for _ in range(N):
	x,y = read_list()
	if 2*x<=y:
		print(x)
	elif 2*y<=x:
		print(y)
	else:
		A = (2*x-y)//3
		B = (2*y-x)//3
		if A+(B+1)*2<=y or (A+1)*2+B<=x:
			print(A+B+1)
		else:
			print(A+B)





