A8165 | Restoration of the Permutation

Let $A={a_{1},a_{2},...,a_{n}}$ be any permutation of the first $n$ natural numbers ${1,2,...,n}$ . You are given a positive integer $k$ and another sequence $B={b_{1},b_{2},...,b_{n}}$ , 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 $X={x_{1},x_{2},...,x_{n}}$ and $Y={y_{1},y_{2},...,y_{n}}$ , 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 $A$ .

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 $B={b_{1},b_{2},...,b_{n}}$ .

Print on a single line $n$ integers of $A={a_{1},a_{2},...,a_{n}}$ such that $A$ is lexicographically minimal. It is guaranteed that the solution exists.