Restoration of the Permutation

1000ms

262144K

Description:

Let A = {a₁, a₂, ..., a_n} be any permutation of the first n natural numbers {1, 2, ..., n}. You are given a positive integer k and another sequence B = {b₁, b₂, ..., b_n}, where b_i is the number of elements a_j in A to the left of the element a_t = i such that a_j ≥ (i + k).

For example, if n = 5, a possible A is {5, 1, 4, 2, 3}. For k = 2, B is given by {1, 2, 1, 0, 0}. But if k = 3, then B = {1, 1, 0, 0, 0}.

For two sequences X = {x₁, x₂, ..., x_n} and Y = {y₁, y₂, ..., y_n}, let i-th elements be the first elements such that x_i ≠ y_i. If x_i < y_i, then X is lexicographically smaller than Y, while if x_i > y_i, then X is lexicographically greater than Y.

Given n, k and B, you need to determine the lexicographically smallest A.

Input:

The first line contains two space separated integers n and k (1 ≤ n ≤ 1000, 1 ≤ k ≤ n). On the second line are n integers specifying the values of B = {b₁, b₂, ..., b_n}.

Output:

Print on a single line n integers of A = {a₁, a₂, ..., a_n} such that A is lexicographically minimal. It is guaranteed that the solution exists.

Sample Input:

5 2
1 2 1 0 0

Sample Output:

4 1 5 2 3

Sample Input:

4 2
1 0 0 0

Sample Output:

2 3 1 4

Informação

Provedor Codeforces

Código CF67B