As we know, the art of splitting workers to separate mineral patches is a tricky one.

There are ~N~ mineral patches in order, each has ~A_i~ minerals to be mined. Our StarCraft player will split ~L~ drones to mine ~L~ contiguous mineral patches.

The StarCraft player notes that for some values of ~L~, over the ~N-L+1~ ways to send drones to mine minerals, the sequence of values corresponding to the mineral patches being mined is the same.

The StarCraft player wishes to find the maximum ~L~ such that some sequence of length ~L~ appears at least ~K~ times among the possible sequences of values that can be mined.

Constraints

~1 \le N \le 20 \cdot 10^3~

~2 \le K \le N~

~0 \le A_i \le 10^6~

Input Specification

The first line will contain two space-separated integers, ~N~ and ~K~.

Each of the next ~N~ lines will contain an integer, the ~A_i~ in order.

Output Specification

Output the maximum ~L~. The input data guarantee that ~L~ is positive.

Sample Input

8 2
1
2
3
2
3
2
3
1

Sample Output

4