Consider an array $A$ consisting of $n$ integers. For each subarray of length $k$, find its minimum value.

Input

• The first line contains two integers $n,k$.
• The second line contains $n$ integers $A_i$.

Output

• Print $n - k + 1$ integers, the $i^{th}$ is the minimum value in the subarray $A_{i,i+k-1}$.

Constraints

• $1 \le n,k \le 10^5$.
• $1 \le A_i \le 10^9$.

Example

Input:

3 2
1 2 3

Output:

1 2