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.
def solve() :
    d, s = map(int, input().split(" "))
    ans = 0 
    if d > s :
        craft = min(d-s, s)
        d -= 2*craft
        s -= craft 
        ans += craft 
    else : 
        craft = min(s-d, d)
        d -= craft
        s -= 2*craft 
        ans += craft 

    craft = min(d, s)//3
    ans += craft*2
    d -= craft*3
    s -= craft*3 
    
    if (d > 0 and s > 1) or (d > 1 and s > 0) :
        ans += 1

    return ans

T = int(input())
ans = []
for _ in range(T) :
    ans.append(solve()) 

for a in ans:
    print(a)
