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 functools import lru_cache
from sys import stdin, stdout
import sys
from math import *
# sys.setrecursionlimit(3*int(1e5))
# input = stdin.readline
# print = stdout.write
 
# @lru_cache()

for __ in range(int(input())):
	n,m=map(int,input().split())
	if(n==m):
		print(ceil(n/2))
	elif(n<=m*2):
		print(n)
	elif(n*2>=m):
		print(m)
	else:
		ans=0
		if(n>m):
			dif=n-m
			ans=dif
			n-=dif*2
			m-=dif
		elif(n<m):
			dif=m-n
			ans=dif
			m-=dif*2
			n-=dif
		print()
		ans+=(n//3)*2
		if(n%3==2):
			ans+=1
		print(ans)
