Minimum of Preceding m Numbers

Given a sequence of n integers, for each element, compute the minimum value among the previous m numbers. If there are fewer than m numbers before the current element, consider all available previous numbers. If no number precedes the current element, output 0.

Note: The current element is not included in the range for computing the minimum.

For example, if n = 5, m = 3 and the sequence is [3, 2, 5, 1, 4] then the answers are:

• For the 1st element: no preceding number, output 0.
• For the 2nd element: consider [3] → minimum is 3.
• For the 3rd element: consider [3, 2] → minimum is 2.
• For the 4th element: consider [3, 2, 5] → minimum is 2.
• For the 5th element: consider [2, 5, 1] → minimum is 1.

inputFormat

The first line contains two integers: n (the number of elements) and m (the number of preceding elements to consider).

The second line contains n space-separated integers representing the sequence.

outputFormat

Output n space-separated integers. The i-th integer is the minimum of the previous m numbers for the i-th element. If there is no preceding number for an element, output 0 for that element.

sample

5 3
3 2 5 1 4

0 3 2 2 1