Sliding Window Distinct Values

You are given an array of n integers. Your task is to calculate the number of distinct values in each window of k elements, from left to right.

Input

The first line contains two integers n and k: the number of elements and the size of the window. Then there are n integers x_1,x_2,\ldots,x_n: the contents of the array.

Output

Print n-k+1 values: the numbers of distinct values.

Constraints

$1 \le k \le n \le 2 \cdot 10^5$

$1 \le x_i \le 10^9$

Example

Input

8 3
1 2 3 2 5 2 2 2

Output

3 2 3 2 2 1