### Problem Statement

You are given a permutation $P_1…P$$N of the set {1, 2, …, N.} You can apply the following operation to this permutation, any number of times (possibly zero): • Choose two indices i,j(1 \le i \le j \le N), such thatK$$\le$ $j−i$ 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

• $2 \le N \le 500,000$
• $1\le K \le N−1$
• $P$ is a permutation of the set {$1$,$2$, …, $N$}.

### Input

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

### Output

Print the lexicographically smallest permutation that can be obtained.

### Sample Output 1

One possible way to obtain the lexicographically smallest permutation is shown below:

• 4231
• 4132
• 3142
• 2143