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 xi≠yi. 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.
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,...,bn}.
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.
5 2
1 2 1 0 0
4 1 5 2 3
4 2
1 0 0 0
2 3 1 4