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(a,b):
    if a == 0 or b == 0:
        print(0)
        return
    if a < b:
        if b >= 2*a:
            print(a)
            return
        else:
            diff = 2*a - b
            sub = diff//3
            if diff%3 == 0:
                sub-=1
            sub+=1
            print(a-sub)
    else:
        if a >= 2*b:
            print(b)
            return
        else:
            diff = 2*b - a
            sub = diff//3
            if diff%3 == 0:
                sub-=1
            sub+=1
            print(b-sub)
            
t = int(input())
for i in range(t):
    a,b = map(int, input().split())
    solve(a,b)
