|2020 ICPC, COMPFEST 12, Indonesia Multi-Provincial Contest (Unrated, Online Mirror, ICPC Rules, Teams Preferred)|
Mr. Chanek is currently participating in a science fair that is popular in town. He finds an exciting puzzle in the fair and wants to solve it.
There are $$$N$$$ atoms numbered from $$$1$$$ to $$$N$$$. These atoms are especially quirky. Initially, each atom is in normal state. Each atom can be in an excited. Exciting atom $$$i$$$ requires $$$D_i$$$ energy. When atom $$$i$$$ is excited, it will give $$$A_i$$$ energy. You can excite any number of atoms (including zero).
These atoms also form a peculiar one-way bond. For each $$$i$$$, $$$(1 \le i < N)$$$, if atom $$$i$$$ is excited, atom $$$E_i$$$ will also be excited at no cost. Initially, $$$E_i$$$ = $$$i+1$$$. Note that atom $$$N$$$ cannot form a bond to any atom.
Mr. Chanek must change exactly $$$K$$$ bonds. Exactly $$$K$$$ times, Mr. Chanek chooses an atom $$$i$$$, $$$(1 \le i < N)$$$ and changes $$$E_i$$$ to a different value other than $$$i$$$ and the current $$$E_i$$$. Note that an atom's bond can remain unchanged or changed more than once. Help Mr. Chanek determine the maximum energy that he can achieve!
note: You must first change exactly $$$K$$$ bonds before you can start exciting atoms.
The first line contains two integers $$$N$$$ $$$K$$$ $$$(4 \le N \le 10^5, 0 \le K < N)$$$, the number of atoms, and the number of bonds that must be changed.
The second line contains $$$N$$$ integers $$$A_i$$$ $$$(1 \le A_i \le 10^6)$$$, which denotes the energy given by atom $$$i$$$ when on excited state.
The third line contains $$$N$$$ integers $$$D_i$$$ $$$(1 \le D_i \le 10^6)$$$, which denotes the energy needed to excite atom $$$i$$$.
A line with an integer that denotes the maximum number of energy that Mr. Chanek can get.
6 1 5 6 7 8 10 2 3 5 6 7 1 10
An optimal solution to change $$$E_5$$$ to 1 and then excite atom 5 with energy 1. It will cause atoms 1, 2, 3, 4, 5 be excited. The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10) - 1 = 35.
Another possible way is to change $$$E_3$$$ to 1 and then exciting atom 3 (which will excite atom 1, 2, 3) and exciting atom 4 (which will excite atom 4, 5, 6). The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10 + 2) - (6 + 7) = 25 which is not optimal.