Problem1913--Restoration of the Permutation

1913: Restoration of the Permutation

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Let A={a1,a2,...,an} 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,...,bn}, where bi is the number of elements aj in A to the left of the element at=i such that aj≥(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,...,xn} and Y={y1,y2,...,yn}, let i-th elements be the first elements such that xiyi. If xi<yi, then X is lexicographically smaller than Y, while if xi>yi, 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≤kn). On the second line are n integers specifying the values of B={b1,b2,...,bn}.

Output

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

Examples
Input
5 2
1 2 1 0 0
Output
4 1 5 2 3 
Input
4 2
1 0 0 0
Output
2 3 1 4 

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