Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
D2. RGB Substring (hard version)

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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.

Input

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 $$$2 \cdot 10^5$$$ ($$$\sum n \le 2 \cdot 10^5$$$).

Output

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 ...".

Example

Input

3 5 2 BGGGG 5 3 RBRGR 5 5 BBBRR

Output

1 0 3

Note

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".

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/03/2021 04:25:57 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|