Sliding Window Mex

You are given an array of n integers. Your task is to calculate the mex of each window of k elements, from left to right. The mex is the smallest nonnegative integer that does not appear in the array. For example, the mex for [3,1,4,3,0,5] is 2.

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 mex values.

Constraints

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

$0 \le x_i \le 10^9$

Example

Input

8 3
1 2 1 0 5 1 1 0

Output

0 3 2 2 0 2