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 j in range(0,t):
    k,l=map(int,input().split())
    s=0
    bb=0
    if(k>l):
        if(k>=2*l):
            print(l)
        else:
            bb=k//2
            if(k%2!=0):
                if(l-bb>=2):
                    bb=bb+1
            s=l//3
            k=k-3*s
            l=l-3*s
            if(l==0):
                print(max(2*s,bb))
            if(l==1):
                print(max(2*s+1,bb))
            if(l==2):
                if(k>=4):
                    print(max(2*s+2,bb))
                else:
                    print(max(2*s+1,bb))
    elif(k==l):
        s=k//3
        k=k-3*s
        l=l-s*3
        if(k>=2 and l>=1):
            print(s*2+1)
            continue
        if(l>=2 and k>=1):
            print(s*2+1)
            continue
        print(s*2)
    else:
        if(l>=2*k):
            print(k)
        else:
            bb=l//2
            if(l%2!=0):
                if(k-bb>=2):
                    bb=bb+1
            s=k//3
            k=k-3*s
            l=l-3*s
            if(k==0):
                print(max(2*s,bb))
            if(k==1):
                print(max(2*s+1,bb))
            if(k==2):
                if(l>=4):
                    print(max(2*s+2,bb))
                else:
                    print(max(2*s+1,bb))
            
            
            
            
