Wide Swap

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

inputFormat

Input

The input is given from Standard Input in the following format:

N K P_1 P_2 ... P_N

outputFormat

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

样例

8 3
4 5 7 8 3 1 2 6

1
2
6
7
5
3
4
8

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