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())):
    s, d = map(int, input().split())
    ans = 0
    if s == d:
        if s % 3 == 0:
            ans = (s // 3)*2
        elif s % 3 == 1:
            ans  = (s // 3)*2
        else:
            ans = (s // 3)*2 +1
    elif s > d:
        if s >= 2*d:
            ans = d
        else:
            ans = s - d
            d -= ans
            if d % 3 == 0:
                ans += (d // 3)*2
            elif d % 3 == 1:
                ans  += (d // 3)*2
            elif d % 3 == 2:
                ans += (d // 3)*2 + 1
    else:
        if d >= 2*s:
            ans = s
        else:
            ans = d - s
            s -= ans
            if s % 3 == 0:
                ans += (s // 3)*2
            elif s % 3 == 1:
                ans += (s // 3)*2
            elif s % 3 == 2:
                ans += (s // 3)*2 + 1
    print(ans)
