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 fractions import Fraction
import bisect
import os
from collections import Counter
import bisect
from collections import defaultdict
import math
import random
import heapq as hq
from math import sqrt
import sys
from functools import reduce, cmp_to_key
from collections import deque
import threading
from itertools import combinations
from io import BytesIO, IOBase
from itertools import accumulate
from queue import Queue

# sys.setrecursionlimit(200000)
# input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
 
def input():    return sys.stdin.readline().strip()
def iinput():   return int(input())
def tinput():   return input().split()
def rinput():   return map(int, tinput())
def rlinput():  return list(rinput())
def get_ints():     return map(int, sys.stdin.readline().strip().split()) 
def get_list():     return list(map(int, sys.stdin.readline().strip().split())) 
def factors(n): return set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
mod = int(1e9)+7


for _ in range(iinput()):
	a, b = get_ints()
	if a>b:
		a, b = b, a

	if b>=2*a:
		print(a)
	else:
		ans = b - a
		a -= ans
		ans += 2*(a//3)
		if (a%3==2):
			print(ans+1)
		else:
			print(ans)