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 ABCD.

In this problem, we define a special substring as a non-empty substring that contains only the same character. For example, B and CC are special substrings of ABBCCC, while ABBC and 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. ABBCCC → ABCCCC) so that we have a special substring CCCC of length 4.
 

Format Input

Input begins with a line containing two integers: N K (1 ≤ K ≤ N ≤ 100000) 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 ∈ [A-Z].

Format Output

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.

Constraints

• 1 ≤ K ≤ N ≤ 100000
• S containing N uppercase alphabetical character, i.e. Si ∈ [A-Z].

Sample Input 1 (Standard Input)

6 4
ABBCCC

Sample Output 1 (Standard Output)
1

Sample Input 2 (Standard Input)

9 6
AABCABBBA

Sample Output 2 (Standard Output)
2

Sample Input 3 (Standard Input)

10 7
BAABAABAAB

Sample Output 3 (Standard Output)
2

Sample Input 4 (Standard Input)

6 2
INNCCC

Sample Output 4 (Standard Output)
0

Explanation:

Explanation for the sample input/output #1
This is the example from the problem description.

Explanation for the sample input/output #2
If we change the fourth and fifth characters of S to B, i.e. AABCABBBA → AABBBBBBA, then S will have a special substring of length 6 which is BBBBBB (AABBBBBBA). In this case, it is not possible to have a special substring of length 6 in S by changing fewer than 2 characters.

Explanation for the sample input/output #3
If we change the fourth and seventh characters of S to A, i.e. BAABAABAAB → BAAAAAAAAB, then S will have a special substring of length 7 which is AAAAAAA (either BAAAAAAAAB or BAAAAAAAAB). In this case, it is not possible to have a special substring of length 7 in S by changing fewer than 2 characters.

Explanation for the sample input/output #4
The string INNCCC already has a special substring of length 2, e.g., NN or CC.