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.
for _ in range(int(input())):
    m,n=map(int,input().split())
    ans =0
    
    if m==2 and n==2:
        ans = 1
    elif m==2 and n==3:
        ans = 1
    elif m==3 and n==2:
        ans = 1
    elif m==0 or n==0:
            ans = 0
    elif m>= 2*n:
        ans = n
    elif n>= 2*m:
        ans = m
    else:
        if n>m:
            m,n=n,m
        ans = 0
        temp = 0
        while m>0 and n>0:
            if m==1 and n==1:
                break
            temp=m//2
            if temp%2==1:
                temp+=1
            if m>n:
                m -= temp
                n -= (temp//2)
            else:
                m-=(temp//2)
                n-= temp
            ans+=(temp//2)
    print(ans)
        
    
    
                
            
    
