RGB Substring (hard version)

PS:此题目与类似的[CF1196D1](https://www.luogu.org/problem/CF1196D1)唯一的不同之处在于数据的范围。 给你$q$组询问（$1 \le q \le 200000$） 每组询问会先给你一个$n$和一个$k$（$1 \le k \le n \le 200000$） 下一行是一个字符串$s$（数据保证$s$只由大写字母$R$、$G$、$B$组成，输入数据保证所有$s$的长度和$ \le 200000$） 现在问你最少修改多少次$s$中的字母（一次只能修改一个字母），才能使得$s$的某一个子串是字符串$RGBRGBRGB...$的子串，同时该子串的长度$ \ge k$。

The only difference between easy and hard versions is the size of the input. You are given a string $ s $ consisting of $ n $ characters, each character is 'R', 'G' or 'B'. You are also given an integer $ k $ . Your task is to change the minimum number of characters in the initial string $ s $ so that after the changes there will be a string of length $ k $ that is a substring of $ s $ , and is also a substring of the infinite string "RGBRGBRGB ...". A string $ a $ is a substring of string $ b $ if there exists a positive integer $ i $ such that $ a_1 = b_i $ , $ a_2 = b_{i + 1} $ , $ a_3 = b_{i + 2} $ , ..., $ a_{|a|} = b_{i + |a| - 1} $ . For example, strings "GBRG", "B", "BR" are substrings of the infinite string "RGBRGBRGB ..." while "GR", "RGR" and "GGG" are not. You have to answer $ q $ independent queries.

The first line of the input contains one integer $ q $ ( $ 1 \le q \le 2 \cdot 10^5 $ ) — the number of queries. Then $ q $ queries follow. The first line of the query contains two integers $ n $ and $ k $ ( $ 1 \le k \le n \le 2 \cdot 10^5 $ ) — the length of the string $ s $ and the length of the substring. The second line of the query contains a string $ s $ consisting of $ n $ characters 'R', 'G' and 'B'. It is guaranteed that the sum of $ n $ over all queries does not exceed $ 2 \cdot 10^5 $ ( $ \sum n \le 2 \cdot 10^5 $ ).

For each query print one integer — the minimum number of characters you need to change in the initial string $ s $ so that after changing there will be a substring of length $ k $ in $ s $ that is also a substring of the infinite string "RGBRGBRGB ...".

3
5 2
BGGGG
5 3
RBRGR
5 5
BBBRR

1
0
3

In the first example, you can change the first character to 'R' and obtain the substring "RG", or change the second character to 'R' and obtain "BR", or change the third, fourth or fifth character to 'B' and obtain "GB". In the second example, the substring is "BRG".