
Score : 2000 points
Problem StatementYou 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}.
InputThe input is given from Standard Input in the following format:
N K
P_1 P_2 ... P_N
OutputPrint the lexicographically smallest permutation that can be obtained.
Sample Input 14 2
4 2 3 1
Sample Output 12
1
4
3
One possible way to obtain the lexicographically smallest permutation is shown below:
4 2 3 1
4 1 3 2
3 1 4 2
2 1 4 3
Sample Input 25 1
5 4 3 2 1
Sample Output 21
2
3
4
5
Sample Input 38 3
4 5 7 8 3 1 2 6
Sample Output 31
2
6
7
5
3
4
8
