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<cstdio>
#include<set>
#include<algorithm>
using namespace std;
const int maxn=5e5+2;
int n,k;
int a[maxn],id[maxn],l[maxn],r[maxn];
set<int> s;
int main(){
	scanf("%d%d",&n,&k);
	for (int i=1;i<=n;i++){
		scanf("%d",&a[i]);
		id[a[i]]=i;
	}
	s.insert(n+1);
	id[n+1]=n+1;
	for (int i=1;i<=n;i++){
		s.insert(a[i]);
		if (i>k) s.erase(a[i-k]);
		int pos=id[*s.upper_bound(a[i])];
		l[i]=l[pos];
		r[l[pos]]=i;
		l[pos]=i;
		r[i]=pos;
	}
	int j=n;
	for (int i=l[n+1];i;i=l[i]) a[i]=j--;
	for (int i=1;i<=n;i++) printf("%d\n",a[i]);
	return 0;
}