A fence consists of $n$ vertical boards. The width of each board is 1 and their heights may vary.

You want to attach a rectangular advertisement to the fence. Your task is to calculate the maximum area of such an advertisement in each window of $k$ vertical boards, from left to right.

Input

The first line contains two integers $n$ and $k$: the width of the fence and the size of the window.

After this, there are $n$ integers $x_1, x_2, \dots, x_n$: the height of each board.

Output

Print $n - k + 1$ integers: the maximum areas of the advertisements.

Constraints

• $1 \le k \le n \le 2 \cdot 10^5$
• $1 \le x_i \le 10^9$

Example

Input:

8 3
4 1 5 3 3 2 4 1

Output:

5 6 9 6 6 4