CF1799F.Halve or Subtract

普及/提高-

通过率：0%

AC君温馨提醒

该题目为【codeforces】题库的题目，您提交的代码将被提交至codeforces进行远程评测，并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供，我们无法保证该服务的稳定性，若提交后无反应，请等待一段时间后再进行重试。

题目描述

You have an array of positive integers $a_1, a_2, \ldots, a_n$ , of length $n$ . You are also given a positive integer $b$ .

You are allowed to perform the following operations (possibly several) times in any order:

Choose some $1 \le i \le n$ , and replace $a_i$ with $\lceil \frac{a_i}{2} \rceil$ . Here, $\lceil x \rceil$ denotes the smallest integer not less than $x$ .
Choose some $1 \le i \le n$ , and replace $a_i$ with $\max(a_i - b, 0)$ .

However, you must also follow these rules:

You can perform at most $k_1$ operations of type 1 in total.
You can perform at most $k_2$ operations of type 2 in total.
For all $1 \le i \le n$ , you can perform at most $1$ operation of type 1 on element $a_i$ .
For all $1 \le i \le n$ , you can perform at most $1$ operation of type 2 on element $a_i$ .

The cost of an array is the sum of its elements. Find the minimum cost of $a$ you can achieve by performing these operations.

输入格式

Input consists of multiple test cases. The first line contains a single integer $t$ , the number of test cases ( $1 \le t \le 5000$ ).

The first line of each test case contains $n$ , $b$ , $k_1$ , and $k_2$ ( $1 \le n \le 5000$ , $1 \le b \le 10^9$ , $0 \le k_1, k_2 \le n$ ).

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ describing the array $a$ ( $1 \le a_i \le 10^9$ ).

It is guaranteed the sum of $n$ over all test cases does not exceed $5000$ .

输出格式

For each test case, print the minimum cost of $a$ you can achieve by performing the operations.

输入输出样例

输入#1

7
3 2 1 1
9 3 5
2 1 2 0
1000000000 1
5 3 1 1
2 8 3 19 3
6 9 4 2
1 2 3 4 5 6
3 10 3 3
1 2 3
5 1 0 0
999999999 999999999 999999999 999999999 999999999
5 5 4 3
5 9 10 7 4

输出#1

说明/提示

In the first test case, you can do the following:

Perform operation 2 on element $a_3$ . It changes from $5$ to $3$ .
Perform operation 1 on element $a_1$ . It changes from $9$ to $5$ .

After these operations, the array is $a = [5, 3, 3]$ has a cost $5 + 3 + 3 = 11$ . We can show that this is the minimum achievable cost.

In the second test case, note that we are not allowed to perform operation 1 more than once on $a_1$ . So it is optimal to apply operation 1 once to each $a_1$ and $a_2$ . Alternatively we could apply operation 1 only once to $a_1$ , since it has no effect on $a_2$ .

In the third test case, here is one way to achieve a cost of $23$ :

Apply operation 1 to $a_4$ . It changes from $19$ to $10$ .
Apply operation 2 to $a_4$ . It changes from $10$ to $7$ .

After these operations, $a = [2, 8, 3, 7, 3]$ . The cost of $a$ is $2 + 8 + 3 + 7 + 3 = 23$ . We can show that this is the minimum achievable cost.

首页