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.
from __future__ import division, print_function
import os,sys
if sys.version_info[0] < 3:
    from __builtin__ import xrange as range;
    from future_builtins import ascii, filter, hex, map, oct, zip
input = lambda: sys.stdin.readline().rstrip("\r\n");
ii = lambda: int(input());vv = lambda: map(int , input().split());
ll = lambda: list(vv());pr = print;pl = lambda l: pr("".join(list(map(str,l))))


for _ in range(ii()):
	n,m = vv()
	pr(min(n,m,(n+m)//3))
