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>
template <typename T>
void print(T pBegin, T pEnd) {
  for (T p = pBegin; p != pEnd; p++) std::cout << *p << " ";
  std::cout << '\n';
}
int main(int argc, const char* argv[]) {
  int n, k;
  std::cin >> n >> k;
  std::vector<int> vec(n);
  std::vector<int> old_vec(n);
  std::vector<int> index_vec(n + 1);
  index_vec[0] = -1;
  for (int i = 0; i < n; i++) {
    std::cin >> vec[i];
    index_vec[vec[i]] = i;
  }
  int h = 10;
  do {
    old_vec = vec;
    for (int i = 1; i < n; i++) {
      if (index_vec[i] - index_vec[i + 1] >= k) {
        std::swap(vec[index_vec[i]], vec[index_vec[i + 1]]);
        std::swap(index_vec[i], index_vec[i + 1]);
      }
    }
  } while (vec != old_vec);
  for (int i = 0; i < n; i++) {
    std::cout << vec[i] << "\n";
  }
  return 0;
}
