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())
for _ in range(t):
    a,b=list(map(int,input().split()))
    if a==b:
        if a==2:
            print(1)
        elif a==3:
            print(2)
        else:
            f=a//3
            if a%3==2:
                print(2*f+1)
            else:
                print(2*f)
    else:
        m=min(a,b)
        n=max(a,b)
        if n>=2*m:
            print(m)
        elif m==0:
            print(0)
        else:
            c=0
            c=c+n-m
            m=m-c
            if m==2:
                print(c+1)
            elif m==3:
                print(c+2)
            else:
                f=m//3
                if m%3==2:
                    c=c+f*2+1
                else:
                    c=c+f*2
                print(c)