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.
""" 616C """
# import math
# import sys
def main():
	n,m= map(int,input().split())
	# a = list(map(int,input().split()))
	mx = max(n,m)
	mn = min(m,n)
	if mx==0 or mn==0:
		print(0)
	elif 2*mn<=mx:
		print(mn)
	else:
		cnt = mx//3
		cnt2 = mn//3
		ans = 2*min(cnt,cnt2)
		# print(ans)
		if cnt==cnt2 and mx%3+mn%3==3:
			ans+=1
		print(ans)
			
		
	return

# main()
def test():
	t = int(input())
	while t:
		main()
		t-=1
test()
