Score : $300$ points

问题描述

商店里有 $N$ 件商品。对于每一件商品 $i = 1, 2, \ldots, N$，第 $i$ 件商品的价格是 $A_i$ 日元（日本货币单位）。

高桥有 $K$ 张优惠券。
每张优惠券可以用于一件商品上。你可以对同一件商品使用任意数量的优惠券，甚至可以不使用优惠券。在价格为 $a$ 日元的商品上使用 $k$ 张优惠券后，你能够以 $\max\lbrace a - kX, 0\rbrace$ 日元的价格购买它。

请输出高桥购买所有商品所需的最小金额。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

There are $N$ items in a shop. For each $i = 1, 2, \ldots, N$, the price of the $i$-th item is $A_i$ yen (the currency of Japan).

Takahashi has $K$ coupons.
Each coupon can be used on one item. You can use any number of coupons, possibly zero, on the same item. Using $k$ coupons on an item with a price of $a$ yen allows you to buy it for $\max\lbrace a - kX, 0\rbrace$ yen.

Print the minimum amount of money Takahashi needs to buy all the items.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq K, X \leq 10^9$
• $1 \leq A_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$ $X$

$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print the answer.

Sample Input 1

5 4 7
8 3 10 5 13

Sample Output 1

12

By using $1$ coupon on the $1$-st item, $1$ coupon on the $3$-rd item, and $2$ coupons on the $5$-th item, Takahashi can:

• buy the $1$-st item for $\max\lbrace A_1-X, 0 \rbrace = 1$ yen,
• buy the $2$-nd item for $\max\lbrace A_2, 0 \rbrace = 3$ yen,
• buy the $3$-rd item for $\max\lbrace A_3-X, 0 \rbrace = 3$ yen,
• buy the $4$-th item for $\max\lbrace A_4, 0 \rbrace = 5$ yen,
• buy the $5$-th item for $\max\lbrace A_5-2X, 0 \rbrace = 0$ yen,

for a total of $1 + 3 + 3 + 5 + 0 = 12$ yen, which is the minimum possible.

Sample Input 2

5 100 7
8 3 10 5 13

Sample Output 2

0

Sample Input 3

20 815 60
2066 3193 2325 4030 3725 1669 1969 763 1653 159 5311 5341 4671 2374 4513 285 810 742 2981 202

Sample Output 3

112

update @ 2024/3/10 10:33:17