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.
import sys

input = sys.stdin.readline

############ ---- Input Functions ---- ############
def inp():
    return (int(input()))
def instr():
    return (str(input()))
def inlt():
    return (list(map(int, input().split())))
# def insr():
#     s = input()
#     return(list(map(int, list(s[:len(s) - 1]))))
def insr():
    s = input()
    return (list(s[:len(s) - 1]))
def invr():
    return (map(int, input().split()))


from collections import Counter


def main():
    t = inp()
    for _ in range(t):
        a, b = inlt()
        a, b = max(a, b), min(a, b)
        if a >= 2 * b:
            print(b)
        else:
            print((a + b) // 3)


if __name__ == '__main__':
    main()
