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.
# -*- coding: utf-8 -*-
"""
Created on Sat Jul 25 15:24:27 2020

@author: Tanmay
"""
def findia(a,b,ans):
    if(a%2==0):
        ansa=a/2
        leftb=b
        if(b>=ansa):
            return (ansa)
        else:
            return (b)
    else:
        ansa=a//2
        leftb=b
        if(b-ansa>=2):
            return (ansa+1)
        elif(b>=ansa):
            return (ansa)
        else:
            return (b)            

def findib(a,b,ansb):
    if(b%2==0):
        ansb=b/2
        lefta=a
        if(a>=ansb):
            return (ansb)
        else:
            return (a)
    else:
        ansb=b//2
        lefta=a
        if(a-ansb>=2):
            return (ansb+1)
        elif(a>=ansb):
            return (ansb)
        else:
            return (a)     

def findi(a,b):
    x=max(a,b)
    y=min(a,b)
    ank=0
    chance=0
    while(x>0 and y>0):
        if(chance%2==0):
         x-=2
         y-=1
         ank+=1
        else:
         x-=1
         y-=2
         ank+=1
        chance+=1
    return (ank)

t=int(input())
for i in range(t):
    a,b=map(int,input().strip().split())
    ans=[]
    ans.append((int(findia(a,b,ans))))
    ans.append((int(findib(a,b,ans))))
    ans.append(int(findi(a,b)))
    print(max(ans))