407981: GYM102956 I Binary Supersonic Utahraptors

Alexey and Boris are playing a game called Binary Supersonic Utahraptors (BSU).

Initially, Alexey has $$$n$$$ utahraptors, and Boris has $$$m$$$ utahraptors. Each utahraptor is either yellow or red.

Then, the players take $$$k$$$ turns described by integers $$$s_1, s_2, \ldots, s_k$$$. The $$$i$$$-th turn is performed as follows. First, Alexey chooses $$$s_i$$$ utahraptors that belong to him and gives them to Boris. Then, Boris chooses $$$s_i$$$ utahraptors that belong to him (the utahraptors that Alexey has just given to him may also be chosen) and gives them to Alexey.

When the $$$k$$$ moves are done, the score of the game is calculated. The score is equal to $$$|a_y - b_r|$$$, where $$$a_y$$$ is the number of yellow utahraptors Alexey has, and $$$b_r$$$ is the number of red utahraptors Boris has. Alexey's goal is to minimize the score, and Boris wants to maximize it.

Write a program that calculates the score of the game if both players use their optimal strategies.

The first line contains three integers $$$n$$$, $$$m$$$, $$$k$$$, the number of utahraptors obtained by Alexey, the number of utahraptors obtained by Boris, and the number of turns in the game ($$$1 \le n, m, k \le 3 \cdot 10^5$$$).

The second line contains $$$n$$$ integers $$$a_i$$$, denoting Alexey's utahraptors ($$$0 \le a_i \le 1$$$). If $$$a_i = 0$$$, then the $$$i$$$-th utahraptor is yellow, otherwise the $$$i$$$-th utahraptor is red.

The third line contains $$$m$$$ integers $$$b_i$$$, denoting Boris's utahraptors in the same manner as described above ($$$0 \le b_i \le 1$$$).

The fourth line contains $$$k$$$ integers $$$s_i$$$, describing the numbers of utahraptors that players give to each other on the $$$i$$$-th turn ($$$1 \le s_i \le \min\{n, m\}$$$).

Print the score of the game if both players play optimally.

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