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.
#!/usr/bin/env python
# coding: utf-8

# In[2]:


import math
t=int(input())
a=[]
for i in range(1,t+1):
    m,n=input().split()
    m=int(m)
    n=int(n)
    if m==0 or n==0:
        a.append(0)
    else:
        if m<=math.floor(n/2):
            a.append(m)
        elif n<=math.floor(m/2):
            a.append(n)
        else:
            a.append(math.floor((m+n)/3))
        
for i in range(0,t):
    print(a[i])


# In[ ]:




