This is an unusual problem in an unusual contest, here is the announcement: http://codeforces.com/blog/entry/73543

You run a string shop. During a day your customers want to buy strings of certain lengths and sometimes satisfying other properties.

Today your first customer asked you if you have a string of length $k$. In fact, you have a string of length $n$ and can cut a string of length $k$ starting at any position out of it. You wonder how many distinct values this string can equal.

Please note that in your shop strings are over an alphabet of size $2$.

Input

The first line contains two integers $n$ and $k$ ($1\leq k\leq n\leq 200\,000$). The second line contains a binary string $s$ of length $n$.

Output

In the only line print the number of distinct substrings of length $k$ of the string $s$.

见题面 Input 部分

见题面 Output 部分

The second sample test represents the de Bruijn sequence of order 3.