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 -

There have to be N bars in the histogram.
The height of any bar in the histogram should be either 0 or M.
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:
\( 1 \le N \le 10^5 \)
\( 1 \le M \le 10^5 \)
\( 1 \le x \le 10^5 \)
\( 1 \le y \le 10^5 \)
\( 0 < a \le b \le N \)
\( 0 \le Height_{i} \le M \)