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.
t=int(input())
k=t
a=list()
ans=list()
while k>0:
    q=input()
    a=q.split()
    x=int(a[0])
    y=int(a[1])
    if x<y:
        if 2*x<y:
            ans.append(x)
        else:
            ans.append(int((x+y)/3))
    else:
        if 2*y<x:
            ans.append(y)
        else:
            ans.append(int((x+y)/3))
    k=k-1
for r in ans:
    print(r)
