Problem Statement

You are given an array of N integers, A1, A2 ,..., AN and an integer B. Return the of count of distinct numbers in all windows of size B.

Formally, return an array of size N-B+1 where i'th element in this array contains number of distinct elements in sequence Ai, Ai+1 ,..., Ai+B-1.

NOTE: if B > N, return an empty array.

Input Format

First argument is an integer array A Second argument is an integer B.

Output Format

Return an integer array.

Example Input

Input 1:

 A = [1, 2, 1, 3, 4, 3]
 B = 3

Input 2:

 A = [1, 1, 2, 2]
 B = 1

Example Output

Output 1:

 [2, 3, 3, 2]

Output 2:

 [1, 1, 1, 1]

Example Explanation

Explanation 1: