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
input=sys.stdin.readline
T=int(input())
for _ in range(T):
    a,b=map(int,input().split())
    a1,b1=a,b
    x=((2*a)-b)//3
    if (a<(2*x) or b<x or x<0):
        x=0
        y=min(b//2,a)

    else:
        a=a-(2*x)
        b=b-x
        y=min(b//2,a)

    y1=((2*b1)-a1)//3
    if (a1<(y1) or b1<2*y1 or y1<0):
        y1=0
        x1=min(b1,a1//2)

    else:
        a1=a1-y1
        b=b-(2*y1)
        x1=min(a1//2,b1)
        

    print(max(x+y,x1+y1))
        
