Unusual Exhibit#6289
A new exhibit has been added to the collection of unusual devices. This device can generate a random permutation of numbers from to . After generating the permutation, it scans and displays n-k+1 numbers on the screen. Each of these numbers represents the count of inversions in the segment from to i+k-1 of the permutation.
An inversion in a permutation is defined as a pair of indices , such that 1 \leq i < j \leq n and p_i > p_j.
The exhibit features two knobs: one to set , the length of the permutation, and the other to set . After adjusting the knobs, visitor Vasya observed the numbers on the screen and now wants to determine the permutation that the device generated. Your task is to assist him in this.
The first line contains two natural numbers and (2 \leq n \leq 10^5, 2 \leq k \leq 5, n \geq k).
The second line contains n-k+1 numbers that appeared on the device's screen. It is guaranteed that the device is working correctly, and there is at least one permutation that can produce these numbers.
Output numbers separated by spaces — the permutation generated by the device. If there are multiple valid permutations, you may output any one of them.
Example 1