Sliding Window Advertisement

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