You are given a string s of length n. Each character is both of the primary k lowercase Latin letters or a question mark.   You are asked to supplant each inquiry mark with one of the primary k lowercase Latin letters so that the accompanying worth is augmented. Let fi be the most extreme length substring of string s, which

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You are given a string s of length n. Each character is both of the primary k lowercase Latin letters or a question mark.  

You are asked to supplant each inquiry mark with one of the primary k lowercase Latin letters so that the accompanying worth is augmented. Let fi be the most extreme length substring of string s, which comprises altogether of the I-th Latin letter. A substring of a string is a bordering aftereffect of that string. Assuming the I-th letter doesn't show up in a string, fi is equivalent to 0. 

The worth of a string s is the base worth among fi for all I from 1 to k.

What is the most extreme worth the string can have?  

Input : The primary line contains two integers n and k (1≤n≤2⋅105; 1≤k≤17) — the length of the string and the number of first Latin letters utilized.The subsequent line contains a string s, comprising of n characters. Each character is both of the principal k lowercase Latin letters or a question mark. 

 Output : Print a solitary integer — the greatest worth of the string after each question mark is supplanted with one of the primary k lowercase Latin letters.