## GUPTA MECHANICAL

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## [Solution] Expected move CodeChef Solution | CodeChef Problem Solution 2022

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

### 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

• $1\le T\le {10}^{5}$