After all the lectures, \(k\) lecturers decided to go taste some cookies. Khust's lecturers love to eat cookies, especially when they want to relax.

There are \(n\) cookies in a row. Each cookie is one of \(10^9\) kinds. Lecturers will take only \(k\) consecutive cookies of the same kind. After every lecturer got his cookie, those \(k\) cookies disappear from the row. They will eat cookies until there's at least one way to choose \(k\) consecutive cookies of the same kind.

Count the number of cookies that one of the lecturers will eat.

Input Specification

First line contains two integers \(n\) and \(k\) \((1 \leq k \leq n \leq 10^6)\) --- the number of cookies and the number of lecturers.

The second line contains \(n\) integers \(A_i\) \((1 \leq A_i \leq 10^9)\) --- kind of the \(i\)-th cookie.

Output Specification

Print one number --- the number of cookies that one of the lecturers will eat.

Sample Input 1

10 3
1 1 2 3 3 3 2 2 1 1

Sample Output 1

3

Note

Initially, there are \(10\) cookies and \(3\) lecturers. \(\texttt{1 1 2 3 3 3 2 2 1 1}\)

Each of the lecturers will take cookies of the third type, and then there will be \(7\) cookies left. \(\texttt{1 1 2 2 2 1 1}\)

After another step, there will be \(4\) cookies left. \(\texttt{1 1 1 1}\)

And in the end, there is only one cookie. \(\texttt{1}\)

So, each lecturer ate \(3\) cookies.