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;
#define ref(i,x,y)for(int i=x;i<=y;++i)
const int N=500010;
int n,k,p[N],q[N],l[N],r[N]; set<int> S;
int main(){
	scanf("%d%d",&n,&k);
	ref(i,1,n)scanf("%d",&p[i]),q[p[i]]=i;
	S.insert(n+1);q[n+1]=n+1;
	ref(i,1,n){
		S.insert(p[i]);if(i>k)S.erase(p[i-k]);
		int id=q[*S.upper_bound(p[i])];
		r[l[id]]=i;l[i]=l[id];l[id]=i;r[i]=id;
	}
	for(int i=l[n+1],j=n;i;i=l[i],--j)p[i]=j;
	ref(i,1,n)printf("%d\n",p[i]);
}