You are given a fair coin and two integers X and N.

You repeatedly flip the coin and perform the following operation based on the result:
If it lands on heads, then X will increase by 1. However, if X = N then X will not change.
If it lands on tails, X will decrease by 1.

You stop as soon as the value of X becomes 1.

Find the expected number of coin flips.

Note that it is guaranteed that under the given constraints, the answer is an integer and does not exceed $2 \cdot 10^{18}$

------ Input Format ------

• The first line contains a single integer T — the number of test cases. Then the test cases follow.
• The first and only line of each test case contains two space separated integers X and N.

------ Output Format ------

For each testcase, output the expected number of coin flips.

------ Constraints ------

$1 ≤ T ≤ 10^{5}$
$1 ≤ X ≤ N ≤ 10^{9}$

----- Sample Input 1 ------
4
1 3
2 2
12 12
568 57800
----- Sample Output 1 ------
0
2
132
65223144

----- explanation 1 ------
In the first test case, $X$ is already $1$. So, the expected number of coin flip in this case is $0$.

In the second test case, if the coin lands on head, $X$ will not change because $X$ is equal to $N$ here. Whenever the coin lands on tail, $X$ will decrease by $1$ and the game ends as $X$ becomes $1$. The expected number of coin flips to get the first tail is $2$. So, the answer for the case is $2$.

见题面

见题面