Searching for Sogang's History

When Seonghyeon (dart) was a freshman, the campus looked very different. For example, the cafeteria was not only in Woojeong Hall but also in Emmaus Hall. Seogang Sikgaek had a Popeyes, and across from Kim Daegeon Hall (K Hall), the stately Gepert Nam Deok-woo Economics Hall (GN Hall) was a run-down student union building (C Hall). The campus did not get any bigger, but the facilities in many of its buildings changed.

Seonghyeon thought that some places on campus now had better facilities than before, but others had worse ones. He wished he could restore the facilities at some of these places to what they were when he was a freshman. So he stood in front of the statue of Father Gepert, the founder of Sogang University, and prayed that the facilities at certain places on campus would be returned to what they were when he entered.

Thirty days after the prayer, Father Gepert suddenly appeared like a mirage. He said that if Seonghyeon chose at most one place on campus, he would restore the facilities there to what they were when Seonghyeon was a freshman. If Seonghyeon chose a place that currently has facilities, those facilities would be replaced with the ones that were there when he was a freshman.

Seonghyeon had prepared for this. For each facility on campus, he had assigned a score for the place as it is now and a score for the facility that was there when he was a freshman. Because of this, he could tell Father Gepert which place he wanted to restore without hesitating for even a second.

Seonghyeon chose at most one place to restore in order to maximize the total score of all places on campus. Find the increase in the total score.

The first line contains the number of places that currently have facilities, $N$, and the number of places that had facilities when Seonghyeon was a freshman, $M$. ($1 \le N,M \le 1\,000$)

The second line contains the scores $a_1, a_2, \cdots, a_N$ that Seonghyeon assigned to the $N$ places that currently have facilities, in order. ($1 \le a_i \le 1\,000$)

The third line contains the scores $b_1, b_2, \cdots, b_M$ that Seonghyeon assigned to the $M$ places that had facilities when he was a freshman, in order. ($1 \le b_i \le 1\,000$)

The current score of place $i$ is $a_i$ if $i \le N$, and $0$ otherwise, since there is no facility there. Likewise, the freshman-era score of place $i$ is $b_i$ if $i \le M$, and $0$ otherwise, since there was no facility there.

On the first line, print the increase in the total score caused by Seonghyeon's choice.