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;

int n, lim, a[500500], cnt;
map<int, int> mp;
vector<int> g[500500];

void dfs(int x) {
  for(int v : g[x]) {
    dfs(v);
  }
  a[x] = ++cnt;
}

int main(void) {
  scanf("%d%d", &n, &lim);
  for(int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  mp[n + 1] = 0;
  for(int i = 1; i <= n; i++) {
    if(i > lim) {
      mp.erase(a[i - lim]);
    }
    g[(mp.upper_bound(a[i]))->second].push_back(i);
    mp[a[i]] = i;
  }
  dfs(0);
  for(int i = 1; i <= n; i++) {
    cout << a[i] << endl;
  }
  return 0;
}
