Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Restoration of the Permutation

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet *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*.

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* = {*b*_{1}, *b*_{2}, ..., *b*_{n}}.

Output

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.

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

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/25/2017 00:33:21 (c3).

Desktop version, switch to mobile version.
User lists

Name |
---|