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())):
    n,m = map(int,input().split())
    if (n==0 or m==0):
        print(0)
    else:
        k1 = max(n,m)
        k2 = min(n,m)
        if(k1%2==0 and k2%2==0):
            f1=k1//2
            k1 = k1-(2*f1)
            if(k2>=f1):
                ans = f1
            else:
                ans = k2
        # elif(k1%2==0 and k2%2!=0):
        #     f1=k1//2
        #     k1 = k1-(2*f1)
        #     if(k2>=f1):
        #         ans = f1
        #         k2 = k2 -f1
        #         if(k2):
        #             ans+=1
        #     else:
        #         ans = k2
        # elif(k1%2!=0 and k2%2==0):
        #     f1=k1//2
        #     k1 = k1-(2*f1)
        #     if(k2>=f1):
        #         ans = f1
        #         k2 = k2 -f1
        #         if(k2):
        #             ans+=1
        #     else:
        #         ans = k2
        else:
            f1=k1//2
            k1 = k1-(2*f1)
            if(k2>=f1):
                ans = f1
                k2 = k2 -f1
                if(k2):
                    ans+=1
            else:
                ans = k2
            
        print(ans)
        