8401번 - Words 다국어

By a word we mean a sequence of capital letters of the English alphabet. The length of a word is the number of letters contained in it. This way, word α = ABAACBBBA is of length 9. By a block within a word we understand maximal consistent subsequence of the same letters. A word is called t-hard, if it contains t blocks. Taking into consideration the word α, it turns out to be 6-hard, because it consists of the following blocks: A|B|AA|C|BBB|A.

If two given words are of the same length, it is possible to check how different they are. Two words of the length n are k-different, if for exactly k positions i (1 ≤ i ≤ n), i'th letter of the first word is different from i'th letter of the second word. Checking two words α and β = AAAABBBBB, it turns out that they are 3-different.

For a given word α, we want to find not too different word β, so that it is not too complicated. Your task is to define, how simple β can be.

Write a program which:

• reads the numbers n, k and a word α of length n;
• determines the minimal value of t, so that there exists a t-hard word β, which is at most k-different from α (which is, there is no k' > k, so that α and β are k'-different);
• writes the answer to the standard output.

In the first line of the standard input there are two integers n, k separated with a single space (1 ≤ n ≤ 1 000, 0 ≤ k ≤ n). They represent adequately: the length of the word α and the allowed level of difference. In the second line there are exactly n capital letters forming the word α.

One integer is to be written to the standard output - t.