You are given an array of n integers and a window length k. A window is a block of k consecutive elements. Sliding the window from the left edge to the right edge produces exactly n - k + 1 windows. For each window, report the largest element it contains.

Output the window maxima in order, from the leftmost window to the rightmost.

Input format

Line 1: two integers n and k separated by a space. Line 2: n space-separated integers, the array values.

Output format

A single line with the n - k + 1 window maxima, separated by single spaces, in left-to-right order.

Constraints

• 1 ≤ k ≤ n ≤ 100000
• -1000000000 ≤ each value ≤ 1000000000
• The answer is uniquely determined: each window has exactly one maximum value.

8 3
1 3 -1 -3 5 3 6 7

3 3 5 5 6 7

4 2
4 4 4 4

4 4 4