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.
import math
from collections import defaultdict
ml=lambda:map(int,input().split())
ll=lambda:list(map(int,input().split()))
ii=lambda:int(input())
ip=lambda:(input())
ips=lambda:input().split()

"""========main code==============="""

t=1
t=ii()
for _ in range(t):
    a,b=ml()
    if(a>b):
        a,b=b,a
    ans=0  
    if(b>2*a):
        print(a)
    else:    
        if(b>a):
            c=min(a,b//2)
            ans+=c
            a-=c
            b-=c*2
        
        print(ans+(a+b)//3)