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 = lambda: sys.stdin.readline().rstrip()
import sys
import math
input = sys.stdin.readline
from collections import deque
from queue import LifoQueue

def binary_search(a, n):
  L = 0
  R = len(a)-1
  while L<=R:
    mid = L+(R-L)//2
    if a[mid]==n:
      return mid
    elif a[mid]<n:
      L = mid+1
    else:
      R = mid-1
  return -1

for _ in range(int(input())):
  sti,dia = map(int, input().split())
  # a = list(map(int, input().split()))
  if sti<dia:
    temp = dia
    dia = sti
    sti = temp
  aa = sti-(2*dia)
  if sti==0 or dia==0:
      print(0)
  else:
      if aa>=0:
        print(dia)
      else:
        print(min(dia,(sti+dia)//3))