You are given a permutation P_1 ... P_N of the set {1, 2, ..., N}.

You can apply the following operation to this permutation, any number of times (possibly zero):

* Choose two indices i,j (1 ≦ i < j ≦ N), such that j - i ≧ K and |P_i - P_j| = 1. Then, swap the values of P_i and P_j.



Among all permutations that can be obtained by applying this operation to the given permutation, find the lexicographically smallest one.

Constraints

* 2≦N≦500,000
* 1≦K≦N-1
* P is a permutation of the set {1, 2, ..., N}.

Input

The input is given from Standard Input in the following format:


N K
P_1 P_2 ... P_N


Output

Print the lexicographically smallest permutation that can be obtained.

Examples

Input

4 2
4 2 3 1


Output

2
1
4
3


Input

5 1
5 4 3 2 1


Output

1
2
3
4
5


Input

8 3
4 5 7 8 3 1 2 6


Output

1
2
6
7
5
3
4
8
#include <bits/stdc++.h>
using namespace std;
int n,k,cnt,a[1000005];
vector<int>v[1000005];
map<int,int>mp;
void dfs(int x)
{
	for(int i=0;i<v[x].size();i++)
    	dfs(v[x][i]);
    cnt++;
	a[x]=cnt;
}
int main()
{
	cin>>n>>k;
	for(int i=1;i<=n;i++)
		cin>>a[i];
	for(int i=1;i<=n;i++)
	{
		if(i>k)
			mp.erase(a[i-k]);
		v[(mp.upper_bound(a[i]))->second].push_back(i);
		mp[a[i]]=i;
	}
	dfs(0);
	for(int i=1;i<=n;i++)
		cout<<a[i]<<endl;

	return 0;
}