Problem Statement

You have $N$ pieces of wood and $M$ sticks, and you have no fences. You will now repeat the following, $0$ or more times: choose one of the $2$ actions below and perform it.

• Action 1: Consume $2$ pieces of wood to create $4$ sticks. This action cannot be performed if you have fewer than $2$ pieces of wood.
• Action 2: Consume $4$ pieces of wood and $2$ sticks to create $3$ fences. This action cannot be performed if you have fewer than $4$ pieces of wood or fewer than $2$ sticks.

Find the maximum possible number of fences you can have after finishing the sequence of actions.

Solve $T$ cases.

Input

$T$
$case_1$
$case_2$
$\vdots$
$case_T$

• $1\leq T\leq 10^5$

$case_i$ represents the $i$-th test case and is given in the following format.

$N\ M$

• $0\leq N\leq 10^9$
• $0\leq M\leq 10^9$
• All input values are integers.

Output

Print on one line the maximum possible number of fences you can have after finishing the actions.

End the output with a newline.

Sample

3
64 0
24 5
0 100

36
15
0