The premise of a popular television show is as follows: a number of notable individuals who lived in Ukraine during a specific period are nominated. Studio guests and viewers discuss various candidates. The most interesting part happens after the show ends: phone numbers are announced on air, and anyone can send an SMS from their phone (costing hryvnia) to vote for their preferred candidate. Each SMS gives the chosen candidate vote. After some time, the SMS votes are counted, and a set number of candidates with the highest votes are declared Great. If there is a tie among candidates that would exceed the specified number of Greats, none of those tied, nor those with lower votes, are considered Great.
A certain socio-political organization wants to ensure that some of its chosen candidates are on the list of Greats. A day before the results are finalized, the organization learns the current vote counts for all candidates, which may not guarantee their desired outcome. Since repeated SMS votes from the same number are not counted, a member of the organization takes to the streets, asking passersby to send an SMS for a specific candidate. The organization reimburses the cost, so the passerby immediately gets their hryvnia back.
Additionally, there is another organization whose aim is to thwart the first organization's plan. A representative from the second organization also asks passersby to send messages for the candidates they support.
Given the amount of money the second organization has, determine the minimum amount the first organization needs to spend to ensure its candidates become Great Ukrainians, even with the best counter-strategy from the second organization.
Assume the population is large enough that each representative can find the needed number of passersby. Furthermore, in the time left before results, no ordinary person will spend their own money on this.
The first line contains integers: (the total number of candidates), (the number of Greats), (the number of candidates promoted by the first organization). The second line contains — the amount of money the second organization has (1 \leq K \leq M \leq N \leq 10^5, 0 \leq S \leq 10^9). The third line contains A_i (i = 1, \ldots, N) — the current vote counts for the candidates (0 \leq A_i \leq 10^9). The fourth line contains B_j (j = 1, \ldots, K) — the indices of candidates that must be made Great.
Output the minimum amount the first organization needs to spend to achieve its goal.
Example 1