CF1279F.New Year and Handle Change

New Year is getting near. So it's time to change handles on codeforces. Mishka wants to change his handle but in such a way that people would not forget who he is.

To make it work, he only allowed to change letters case. More formally, during one handle change he can choose any segment of his handle $[i; i + l - 1]$ and apply tolower or toupper to all letters of his handle on this segment (more fomally, replace all uppercase letters with corresponding lowercase or vice versa). The length $l$ is fixed for all changes.

Because it is not allowed to change codeforces handle too often, Mishka can perform at most $k$ such operations. What is the minimum value of $min(lower, upper)$ (where $lower$ is the number of lowercase letters, and $upper$ is the number of uppercase letters) can be obtained after optimal sequence of changes?

新年临近，是时候在 Codeforces 上更换昵称了。Mishka 想要更改自己的昵称，但希望人们仍能记住他是谁。

为实现这一目标，他只允许更改字母的大小写。更准确地说，在一次昵称修改操作中，他可以选择昵称的任意一个子段 $[i; i + l - 1]$，并对该子段内所有字母统一执行 tolower 或 toupper 操作（即：将所有大写字母替换为对应的小写字母，或反之）。每次操作所选子段的长度 $l$ 是固定的。

由于 Codeforces 不允许过于频繁地更改昵称，Mishka 最多只能执行 $k$ 次这样的操作。在经过最优的操作序列后，$min(lower, upper)$（其中 $lower$ 表示小写字母的数量，$upper$ 表示大写字母的数量）所能达到的最小值是多少？

The first line of the input contains three integers $n, k$ and $l$ ($1 \le n, k, l \le 10^6, l \le n)$ — the length of Mishka's handle, the number of changes and the length of the segment.

The second line of the input contains one string $s$, consisting of $n$ lowercase and uppercase Latin letters — Mishka's handle.

输入的第一行包含三个整数 $n, k$ 和 $l$（$1 \le n, k, l \le 10^6, l \le n$）——分别表示 Mishka 用户名的长度、修改次数以及区间长度。

输入的第二行包含一个字符串 $s$，由 $n$ 个大小写拉丁字母组成——即 Mishka 的用户名。

Print one integer — the minimum value of $min(lower, upper)$ after that Mishka change his handle at most $k$ times in a way described in the problem statement.

输出一个整数——在 Mishka 按照题目描述的方式最多更改用户名 $k$ 次后，$min(lower, upper)$ 的最小可能值。