Histograms are generally fun to play with. But not all histograms are complete. Making a normal histogram complete, is not such an easy task. We will attempt to do it here.

Let us first define a complete histogram. A histogram is complete iff it satisfies the following conditions -

1. There have to be N bars in the histogram.
2. The height of any bar in the histogram should be either 0 or M.
3. For any pair of $i, j$, if (($i == 1$ or $Height_{i - 1} != Height_i$) and ($j == N$ or $Height_{j + 1} != Height_j$) and ($Height_k == Height_i$, for all $i \le k \le j$)) holds, then $a \le j - i + 1 \le b$ should hold.

You are given a histogram, which may or may not be complete. It has to be converted into a complete histogram with minimum cost incurred. You are allowed to increase or decrease height of any bar in it. The cost of increasing any bar by unit height costs x and decreasing any bar by unit height costs y.

Input:
The first line of the input contains 6 integers, $N, M, a, b, x, y$, as mentioned in the problem statement.
The second line contains N integers, representing an array A of size N, where the element at index i represents $Height_i$.

Output:
A single integer representing the minimum cost needed to convert the histogram into a complete histogram. Print -1 if it is not possible to make a complete histogram.

Constraints:
$1 \le N \le 10^5$
$1 \le M \le 10^5$
$1 \le x \le 10^5$
$1 \le y \le 10^5$
$0 < a \le b \le N$
$0 \le Height_{i} \le M$