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.
def bin(n, a, b):
    l = 0
    r = n
    while r - l > 1:
        lop = (r + l) // 2
        sw = (a + b - 3 * lop) // 3
        if a < 2 * lop + sw or b < 2 * sw + lop:
            r = lop
        else:
            l = lop
    if a >= 2 * lop + sw and b >= 2 * sw + lop:
        return lop + sw
    else:
        sw1 = (a + b - 3 * r) // 3
        if a >= 2 * r + sw1 and b >= 2 * sw1 + r:
            return r + sw1
        sw2 = (a + b - 3 * l) // 3
        if a >= 2 * l + sw2 and b >= 2 * sw2 + l:
            return l + sw2
        return 0
        
        

t = int(input())
while t:
    a, b = map(int, input().split())
    print(bin(10**9, a, b))
    t -= 1
