Given an array $A$ of $n$ integers indexed $0,1,...,n-1$. You will perform the following operation $n$ times:
- Delete the maximum elements among elements with indices $0, k, 2 \times k,...$, if there are multiple maximum elements, delete the one with the smallest index.
Find the deleted element at each step.
### Input
- The first line contains 2 integers $n, k$.
- The second line contains $n$ integers $A_i$.
### Output
- Print the deleted element after each step.
### Constraints
- $1 \le k \le n \le 10^5$.
- $1 \le A_i \le n$.
### Example
Input:
```
10 3
2 3 1 9 10 4 5 6 1 5
```
Output:
```
9
10
4
5
6
2
5
3
1
1
```
