D. Berserk And Fireball
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

There are $n$ warriors in a row. The power of the $i$-th warrior is $a_i$. All powers are pairwise distinct.

You have two types of spells which you may cast:

1. Fireball: you spend $x$ mana and destroy exactly $k$ consecutive warriors;
2. Berserk: you spend $y$ mana, choose two consecutive warriors, and the warrior with greater power destroys the warrior with smaller power.

For example, let the powers of warriors be $[2, 3, 7, 8, 11, 5, 4]$, and $k = 3$. If you cast Berserk on warriors with powers $8$ and $11$, the resulting sequence of powers becomes $[2, 3, 7, 11, 5, 4]$. Then, for example, if you cast Fireball on consecutive warriors with powers $[7, 11, 5]$, the resulting sequence of powers becomes $[2, 3, 4]$.

You want to turn the current sequence of warriors powers $a_1, a_2, \dots, a_n$ into $b_1, b_2, \dots, b_m$. Calculate the minimum amount of mana you need to spend on it.

Input

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 2 \cdot 10^5$) — the length of sequence $a$ and the length of sequence $b$ respectively.

The second line contains three integers $x, k, y$ ($1 \le x, y, \le 10^9; 1 \le k \le n$) — the cost of fireball, the range of fireball and the cost of berserk respectively.

The third line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$). It is guaranteed that all integers $a_i$ are pairwise distinct.

The fourth line contains $m$ integers $b_1, b_2, \dots, b_m$ ($1 \le b_i \le n$). It is guaranteed that all integers $b_i$ are pairwise distinct.

Output

Print the minimum amount of mana for turning the sequnce $a_1, a_2, \dots, a_n$ into $b_1, b_2, \dots, b_m$, or $-1$ if it is impossible.

Examples
Input
5 2
5 2 3
3 1 4 5 2
3 5

Output
8

Input
4 4
5 1 4
4 3 1 2
2 4 3 1

Output
-1

Input
4 4
2 1 11
1 3 2 4
1 3 2 4

Output
0