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×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 Ai.
### Output
- Print the deleted element after each step.
### Constraints
- 1≤k≤n≤105.
- 1≤Ai≤n.
### Example
Input:
10323191045615
Output:
91045625311
