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 ford(i,a,b) for(int i=(a);i>=b;i--)
#define rep1(i,a,b) for(int i=(a);(i)<=(b);(i)++)
#define rep(i,a,b) for(int i=(a);(i)<(b);(i)++)
#define ll long long
#define mpi map<int,int>
#define N 500005
#define pql priority_queue<ll>
#define all(v) (v).begin(),(v).end()
#define str stringstream
using namespace std;
int n,k,a[N],cnt;
vector<int> g[N];
mpi mp; 
void dfs(int x) {
	for(auto v:g[x])
    	dfs(v);
    cnt++;
	a[x]=cnt;
}
int main() {
	cin>>n>>k;
	rep1(i,1,n)cin>>a[i];
	rep1(i,1,n) {
    	if(i>k)mp.erase(a[i-k]);
    	g[(mp.upper_bound(a[i]))->second].push_back(i);
		mp[a[i]]=i;
	}
	dfs(0);
	rep1(i,1,n)cout<<a[i]<<"\n";
	return 0;
}