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A substring of a string is a contiguous sequence of characters from the string. For example,
BC is a substring of
ABCD which starts from the second character of
ABCD. Another example,
ABC is a substring of
ABCD which starts from the first character of
ABCD. Note that
ABCD itself is also a substring of
In this problem, we define a special substring as a non-empty substring that contains only the same character. For example,
CC are special substrings of
BC are not special substrings.
You are given a string S of length N and an integer K. Your task is to determine the minimum number of characters of S that need to be changed such that there exists a special substring of length K in S.
For example, let N = 6, K = 4, and S =
ABBCCC. In this example, we only need to change the third character of S to C (i.e.
ABCCCC) so that we have a special substring
CCCC of length 4.
Input begins with a line containing two integers: N K (1 ≤ K ≤ N ≤ 100 000) representing the length of the string and the length of a special substring that should be produced, respectively. The next line contains a string S containing N uppercase alphabetical character, i.e. Si ∈ [
Output in a line an integer representing the minimum number of characters of S that need to be changed such that there exists a special substring of length K in the given S.
6 4 ABBCCC
9 6 AABCABBBA
If we change the fourth and fifth characters of S to B, i.e.
AABBBBBBA, then S will have a special substring of length 6 which is
AABBBBBBA). In this case, it is not possible to have a special substring of length 6 in S by changing fewer than 2 characters.
10 7 BAABAABAAB
If we change the fourth and seventh characters of S to A, i.e.
BAAAAAAAAB, then S will have a special substring of length 7 which is
BAAAAAAAAB). In this case, it is not possible to have a special substring of length 7 in S by changing fewer than 2 characters.
6 2 INNCCC
INNCCC already has a special substring of length 2, e.g.,