You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 256.0 MB

# Problem
There are $$$n$$$ chests. The $$$i$$$-th chest contains $$$a_i$$$ coins. You need to open all $$$n$$$ chests in order from chest $$$1$$$ to chest $$$n$$$.

There are two types of keys you can use to open a chest:

- a good key, which costs $$$k$$$ coins to use;
- a bad key, which does not cost any coins, but will halve all the coins in each unopened chest, including the chest it is about to open. The halving operation will round down to the nearest integer for each chest halved. In other words using a bad key to open chest $$$i$$$ will do $$$a_i = \lfloor{\frac{a_i}{2}\rfloor}$$$, $$$a_{i+1} = \lfloor\frac{a_{i+1}}{2}\rfloor, \dots, a_n = \lfloor \frac{a_n}{2}\rfloor$$$;
- any key (both good and bad) breaks after a usage, that is, it is a one-time use.

You need to use in total $$$n$$$ keys, one for each chest. Initially, you have no coins and no keys. If you want to use a good key, then you need to buy it.

During the process, you are allowed to go into debt; for example, if you have $$$1$$$ coin, you are allowed to buy a good key worth $$$k=3$$$ coins, and your balance will become $$$-2$$$ coins.

Find the maximum number of coins you can have after opening all $$$n$$$ chests in order from chest $$$1$$$ to chest $$$n$$$.

## Input Format
The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 10^5$$$; $$$0 \leq k \leq 10^9$$$) — the number of chests and the cost of a good key respectively.

The second line of each test case contains $$$n$$$ integers $$$a_i$$$ ($$$0 \leq a_i \leq 10^9$$$)  — the amount of coins in each chest.

The sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

## Output Format
For each test case output a single integer  — the maximum number of coins you can obtain after opening the chests in order from chest $$$1$$$ to chest $$$n$$$.

Please note, that the answer for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language (like long long for C++).

## Examples
```input
5
4 5
10 10 3 1
1 2
1
3 12
10 10 29
12 51
5 74 89 45 18 69 67 67 11 96 23 59
2 57
85 60
```
```output
11
0
13
60
58
```

## Note
In the first test case, one possible strategy is as follows:

- Buy a good key for $$$5$$$ coins, and open chest $$$1$$$, receiving $$$10$$$ coins. Your current balance is $$$0 + 10 - 5 = 5$$$ coins.
- Buy a good key for $$$5$$$ coins, and open chest $$$2$$$, receiving $$$10$$$ coins. Your current balance is $$$5 + 10 - 5 = 10$$$ coins.
- Use a bad key and open chest $$$3$$$. As a result of using a bad key, the number of coins in chest $$$3$$$ becomes $$$\left\lfloor \frac{3}{2} \right\rfloor = 1$$$, and the number of coins in chest $$$4$$$ becomes $$$\left\lfloor \frac{1}{2} \right\rfloor = 0$$$. Your current balance is $$$10 + 1 = 11$$$.
- Use a bad key and open chest $$$4$$$. As a result of using a bad key, the number of coins in chest $$$4$$$ becomes $$$\left\lfloor \frac{0}{2} \right\rfloor = 0$$$. Your current balance is $$$11 + 0 = 11$$$.

Now solve the problem and return the code.