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 Fri Jun 12 08:53:45 2020

@author: SuperDY
"""
def cal(x,y,now):
    y-=2*now
    x-=now
    return now+min(x//2,y)
t=int(input())
for o in range(t):
    s=input().split()
    n,m=int(s[0]),int(s[1])
    if n>m:
        n,m=m,n
    l,r=0,min(n,m//2)
    while r-l>10:
        m1=(l+r)>>1
        m2=(m1+r)>>1
        if cal(n,m,m1)>cal(n,m,m2):
            r=m2
        else :
            l=m1
    ans=0
    for i in range(l,r+1):
        ans=max(ans,cal(n,m,i))
    print(int(ans))
            