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
sys.setrecursionlimit(1500)
t=int(input())
q=[]
while(t>0):
    a,b=map(int,input().split())
    if (a==0) or (b==0):
        q.append("0")
    elif a>b:
        c=a//2
        if abs(a-b)==1:
            [q.append(a+1) if b<=c else q.append(c+1)]
        else:[q.append(a) if a<=c else q.append(c)]
    else:
        c=b//2
        if abs(a-b)==1:
            [q.append(b+1) if b<=c else q.append(c+1)]
        else:[q.append(b) if b<=c else q.append(c)]
    t-=1
[print(l) for l in q]
			  	  		  		   	 		 	  	  		