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.
# Contest No.: Edu89
# Problem No.: A
# Solver:      JEMINI
# Date:        20200611

import sys
import heapq

def main():
    t = int(input())
    for _ in range(t):
        a, b = map(int, sys.stdin.readline().split())
        ans = 0
        if a > b:
            a, b = b, a

        if 2 * a <= b:
            print(a)
            continue
        
        div = (2 * a - b) // 3
        ans = div * 2
        a -= div * 3
        b -= div * 3
        if a >= 1:
            ans += b // 2
        
        print(ans)
    return

if __name__ == "__main__":
    main()