Expected move

 You are given a fair coin and two integers 

X$X$ and N$N$.

You repeatedly flip the coin and perform the following operation based on the result:

• If it lands on heads, then X$X$ will increase by 1$1$. However, if X=N$X=N$ then X$X$ will not change.
• If it lands on tails, X$X$ will decrease by 1$1$.

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

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⋅1018$2\cdot {10}^{18}$

Input Format

• The first line contains a single integer T$T$ — 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$X$ and N$N$.

Output Format

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

Constraints

• 1≤T≤105$1\le T\le {10}^5$
• 1≤X≤N≤109$1\le X\le N\le {10}^9$

Sample Input 1 

4
1 3
2 2
12 12
568 57800

Sample Output 1 

0
2
132
65223144

Explanation

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

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