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;

const int MAXN = 505050;

int N,K;
int arr[MAXN];
int pos[MAXN];
int mpos[MAXN];
int temppos[MAXN];

void merge(int a,int b,int c){
	int i = a,j = b+1,k = a;
	mpos[b] = pos[b];
	for(int l=b-1;l>=a;l--){
		mpos[l] = min(pos[l],mpos[l+1]);
	}
	while(i<=b&&j<=c){
		if(mpos[i] < pos[j] + K){
			temppos[k++] = pos[i++];
		}
		else temppos[k++] = pos[j++];
	}
	while(i<=b) temppos[k++] = pos[i++];
	while(j<=c) temppos[k++] = pos[j++];
	for(int k=a;k<=c;k++){
		pos[k] = temppos[k];
	}
}

void msort(int s,int e){
	if(s==e) return;
	int m = (s+e)>>1;
	msort(s,m); 
	msort(m+1,e);
	merge(s,m,e);
}



int main(){
	scanf("%d %d",&N,&K);
	for(int i=1;i<=N;i++){
		int temp;
		scanf("%d",&temp);
		pos[temp] = i;
	}
	msort(1,N);
	for(int i=1;i<=N;i++){
		arr[pos[i]] = i;
	}
	for(int i=1;i<=N;i++){
		printf("%d\n",arr[i]);
	}
	return 0;
}
