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.
from sys import stdin, stdout

read = stdin.readline
write = stdout.write
flush = stdout.flush
xr = xrange

def solve():
	a,b = map(int,read().split())
	ans = 0
	while (a > 1 and b > 1):
		if a >= b:
			a -= 2
			b -= 1
			ans += 1
		elif b > a:
			b -= 2
			a -= 1
			ans += 1
	print a, b,
	if a > 1 and b == 1:
		ans += 1
	elif b > 1 and a == 1:
		ans += 1
	print ans

t = int(read())
for _ in xr(t):
	solve()