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;
template <class T>
inline bool chkmax(T& a, T b) {
  return a < b ? a = b, 1 : 0;
}
template <class T>
inline bool chkmin(T& a, T b) {
  return a > b ? a = b, 1 : 0;
}
template <typename T>
inline T& read(T& x) {
  static char c;
  bool flag = 0;
  while (!isdigit(c = getchar()))
    if (c == '-') flag = 1;
  for (x = c - '0'; isdigit(c = getchar()); (x *= 10) += c - '0')
    ;
  if (flag) x = -x;
  return x;
}
const int maxn = 500010;
int n, k, t[maxn], p[maxn], ind[maxn];
int head[maxn], nxt[maxn], to[maxn], e;
void ae(int x, int y) {
  to[++e] = y;
  nxt[e] = head[x];
  head[x] = e;
}
namespace SGT {
int T[maxn * 3];
void pushup(int h) { T[h] = max(T[h << 1], T[h << 1 | 1]); }
void update(int h, int l, int r, int p, int x) {
  if (l == r) {
    T[h] = x;
    return;
  }
  if (p <= ((l + r) >> 1))
    update(h << 1, l, ((l + r) >> 1), p, x);
  else
    update(h << 1 | 1, ((l + r) >> 1) + 1, r, p, x);
  pushup(h);
}
int query(int h, int l, int r, int L, int R) {
  if (L <= l && r <= R) return T[h];
  int ret = 0;
  if (L <= ((l + r) >> 1)) chkmax(ret, query(h << 1, l, ((l + r) >> 1), L, R));
  if (R > ((l + r) >> 1))
    chkmax(ret, query(h << 1 | 1, ((l + r) >> 1) + 1, r, L, R));
  return ret;
}
}  // namespace SGT
using namespace SGT;
priority_queue<int, vector<int>, greater<int> > q;
int main() {
  read(n);
  read(k);
  for (int i = 1; i <= n; i++) t[read(p[i])] = i;
  for (int i = 1; i <= n; i++) {
    int pre = query(1, 1, n, t[i] + 1, t[i] + k - 1);
    update(1, 1, n, t[i], i);
    if (pre) ae(t[pre], t[i]), ++ind[t[i]];
  }
  for (int i = 1; i <= n; i++)
    if (!ind[i]) q.push(i);
  for (int i = 1; i <= n; i++) {
    int u = q.top();
    q.pop();
    t[i] = u;
    for (int j = head[u]; j; j = nxt[j]) {
      int v = to[j];
      if (!--ind[v]) q.push(v);
    }
  }
  for (int i = 1; i <= n; i++) p[t[i]] = i;
  for (int i = 1; i <= n; i++) printf("%d\n", p[i]);
  return 0;
}
