Restoration of the Permutation

Restoration of the Permutation

Time Limit: 1000ms

Memory Limit: 262144KB

This problem will be judged on CodeForces. Original ID: 67B
64-bit integer IO format: %I64d      Java class name: (Any)

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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

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 

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstdlib>

using namespace std;

int main()
{
    int n,k;
    int i,j,t;
    int a[1010],b[1010];
    while(cin>>n>>k)
    {
        for(i=1;i<=n;i++)
        {
            cin>>a[i];
        }
        for(i=1;i<=n;i++)
        {
            j=1;
            while(a[j]!=0)
            {
                j++;
            }
            b[i]=j;
            a[j]--;
            for(t=1;t+k<=j;t++)
            {
                a[t]--;
            }
        }
        for(i=1;i<n;i++)
        {
            cout<<b[i]<<' ';
        }
        cout<<b[n]<<endl;
    }
    return 0;
}