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 $k$ $(1\le k\le n\le {10}^6)$ --- the number of cookies and the number of lecturers.

The second line contains $n$ integers $A_i$ $(1\le A_i\le {10}^9)$ --- 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. $\mathtt{\text{1 1 2 3 3 3 2 2 1 1}}$

Each of the lecturers will take cookies of the third type, and then there will be $7$ cookies left. $\mathtt{\text{1 1 2 2 2 1 1}}$

After another step, there will be $4$ cookies left. $\mathtt{\text{1 1 1 1}}$

And in the end, there is only one cookie. $\mathtt{\text{1}}$

So, each lecturer ate $3$ cookies.