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
t = int(input())

def equalans(a):
    ans = int(math.floor(a/3))*2
    if a%3==2:
        ans+=1
    return ans

for i in range(t):
    inp = input().split(" ")
    a, b = int(inp[0]), int(inp[1])

    if a==0 or b==0: 
        print(0)
        continue
    if a == b:
        print(equalans(a))
        continue

    if b > a:
        t = a
        a = b
        b = t
    
    if a>=2*b:
        print(b)
        continue

    ex = a%b
    a -= 2*ex
    b -= ex
    print(equalans(a)+ex)


