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>
#define N 505000
using namespace std;

int n,k,a[N],L[N],R[N],mn[N],an[N],pos[N],sz=500,tot,ans[N];
int now,res,p;

void RE(int w){
	now=res=1e8;
	for (int i=L[w];i<=R[w];++i){
		if (now-a[i]>=k) res=a[i],p=i;
		now=min(now,a[i]);
	}
	mn[w]=now, an[w]=res, pos[w]=p;
}

int doit(){
	now=res=1e8;
	for (int i=1;i<=tot;++i){
		if (now-an[i]>=k) res=an[i],p=i;
		now=min(now,mn[i]);
	}
	return pos[p];
}

int main(){
	cin>>n>>k; for (int i=1,x;i<=n;++i) scanf("%d",&x), a[x]=i; tot=(n-1)/sz+1;
	for (int i=1;i<=tot;++i) L[i]=i*sz-sz+1, R[i]=min(n,i*sz), RE(i);
	for (int i=1,p;i<=n;++i) ans[a[p=doit()]]=i, a[p]=1e8, RE((p-1)/sz+1);
	for (int i=1;i<=n;++i) printf("%d\n",ans[i]);
}