시간 제한메모리 제한제출정답맞힌 사람정답 비율
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문제

Alice와 Bob은 수가 적힌 카드를 이용한 게임을 즐겨한다.

지금 Bob은 $n$장의 카드, Alice는 $m$장의 카드를 갖고 있고, 각 카드에는 양의 정수가 적혀있다.

두 사람은 각자 자신이 가진 카드 중 $k$장씩을 선택하여 이에 적힌 $k$개의 정수를 더하여 본인의 점수를 계산하기로 했다. 이 때 Bob의 점수를 $B$, Alice의 점수를 $A$라 하자. 이 게임은 두 사람이 어떤 카드를 선택하는지에 따라 $B$, $A$ 값이 바뀌므로 두 사람은 문득 $|B - A|$의 최솟값과 최댓값이 궁금해졌다.

예를 들어 $k = 2$ 이고 Bob은 $[2, 3, 5]$가 적힌 카드를, Alice는 $[1, 4, 8, 9]$가 적힌 카드를 가지고 있다고 하자.

  • Bob이 두 장을 선택하여 달성 가능한 점수는 $5$, $7$, $8$ 셋 중 하나이다.
  • Alice가 두 장을 선택하여 달성 가능한 점수는 $5$, $9$, $10$, $12$, $13$, $17$ 중 하나이다.
  • 이 때 $|B - A|$의 최솟값은 $0$이며 ($B = A = 5$) 최댓값은 $12$이다 ($B = 5$, $A = 17$).

입력으로 $k$와 두 사람이 가진 카드에 적힌 수들이 주어졌을 때, 달성 가능한 $|B - A|$의 최솟값과 최댓값을 구해보자.

입력

첫 줄에 테스트 케이스의 수 $T$가 주어진다.

각 케이스의 입력은 세 줄에 나누어 주어진다. 첫 줄에 $n$, $m$, $k$가 공백으로 구분되어 주어진다. 둘째 줄에 Bob이 가진 카드에 적힌 수 $n$개가 공백으로 구분되어 주어진다. 셋째 줄에 Alice가 가진 카드에 적힌 수 $m$개가 공백으로 구분되어 주어진다.

출력

각 테스트 케이스의 정답을 최솟값, 최댓값 순으로 공백으로 구분하여 각 줄에 출력한다.

제한

  • $1 ≤ T ≤ 5$
  • $2 ≤ n, m ≤ 20$
  • $2 ≤ k ≤ \min{(n, m, 10)}$
  • $1 ≤ $ 각 카드에 적힌 수 $ ≤ 10^8$

예제 입력 1

4
3 4 2
2 3 5
1 4 8 9
3 4 3
2 3 5
1 4 8 9
5 5 3
1 2 1 2 3
3 2 3 2 1
2 2 2
2022 2021
2022 2000

예제 출력 1

0 12
3 11
0 4
21 21

예제 1-2: 본문에서 다루었다.

예제 3: 이 경우 Bob, Alice가 각각 $(1, 2, 3)$을 골라 $6$점씩 달성하면 점수 차이의 최솟값은 $0$이다. Bob이 $(1, 1, 2) = 4$점, Alice가 $(2, 3, 3) = 8$점을 달성하면 최댓값은 $4$가 된다.

예제 4: 이 경우 Bob이 달성 가능한 점수는 $(2022+2021)$이고 Alice가 달성 가능한 점수는 $(2022+2000)$이므로 두 점수 차이의 최솟값과 최댓값은 $21$이다.

[{"problem_id":"24432","problem_lang":"0","title":"\uce74\ub4dc \ub180\uc774","description":"<p>Alice\uc640 Bob\uc740 \uc218\uac00 \uc801\ud78c \uce74\ub4dc\ub97c \uc774\uc6a9\ud55c \uac8c\uc784\uc744 \uc990\uaca8\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc9c0\uae08 Bob\uc740 $n$\uc7a5\uc758 \uce74\ub4dc, Alice\ub294 $m$\uc7a5\uc758 \uce74\ub4dc\ub97c \uac16\uace0 \uc788\uace0, \uac01 \uce74\ub4dc\uc5d0\ub294 \uc591\uc758 \uc815\uc218\uac00 \uc801\ud600\uc788\ub2e4.<\/p>\r\n\r\n<p>\ub450 \uc0ac\ub78c\uc740 \uac01\uc790 \uc790\uc2e0\uc774 \uac00\uc9c4 \uce74\ub4dc \uc911 $k$\uc7a5\uc529\uc744 \uc120\ud0dd\ud558\uc5ec \uc774\uc5d0 \uc801\ud78c $k$\uac1c\uc758 \uc815\uc218\ub97c \ub354\ud558\uc5ec \ubcf8\uc778\uc758 \uc810\uc218\ub97c \uacc4\uc0b0\ud558\uae30\ub85c \ud588\ub2e4. \uc774 \ub54c Bob\uc758 \uc810\uc218\ub97c $B$, Alice\uc758 \uc810\uc218\ub97c $A$\ub77c \ud558\uc790. \uc774 \uac8c\uc784\uc740 \ub450 \uc0ac\ub78c\uc774 \uc5b4\ub5a4 \uce74\ub4dc\ub97c \uc120\ud0dd\ud558\ub294\uc9c0\uc5d0 \ub530\ub77c $B$, $A$ \uac12\uc774 \ubc14\ub00c\ubbc0\ub85c \ub450 \uc0ac\ub78c\uc740 \ubb38\ub4dd $|B - A|$\uc758 \ucd5c\uc19f\uac12\uacfc \ucd5c\ub313\uac12\uc774 \uad81\uae08\ud574\uc84c\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4 $k = 2$ \uc774\uace0 Bob\uc740 $[2, 3, 5]$\uac00 \uc801\ud78c \uce74\ub4dc\ub97c, Alice\ub294 $[1, 4, 8, 9]$\uac00 \uc801\ud78c \uce74\ub4dc\ub97c \uac00\uc9c0\uace0 \uc788\ub2e4\uace0 \ud558\uc790.<\/p>\r\n\r\n<ul>\r\n\t<li>Bob\uc774 \ub450 \uc7a5\uc744 \uc120\ud0dd\ud558\uc5ec \ub2ec\uc131 \uac00\ub2a5\ud55c \uc810\uc218\ub294 $5$, $7$, $8$ \uc14b \uc911 \ud558\ub098\uc774\ub2e4.<\/li>\r\n\t<li>Alice\uac00 \ub450 \uc7a5\uc744 \uc120\ud0dd\ud558\uc5ec \ub2ec\uc131 \uac00\ub2a5\ud55c \uc810\uc218\ub294 $5$, $9$, $10$, $12$, $13$, $17$ \uc911 \ud558\ub098\uc774\ub2e4.<\/li>\r\n\t<li>\uc774 \ub54c $|B - A|$\uc758 \ucd5c\uc19f\uac12\uc740 $0$\uc774\uba70 ($B = A = 5$) \ucd5c\ub313\uac12\uc740 $12$\uc774\ub2e4 ($B = 5$, $A = 17$).<\/li>\r\n<\/ul>\r\n\r\n<p>\uc785\ub825\uc73c\ub85c $k$\uc640 \ub450 \uc0ac\ub78c\uc774 \uac00\uc9c4 \uce74\ub4dc\uc5d0 \uc801\ud78c \uc218\ub4e4\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ub2ec\uc131 \uac00\ub2a5\ud55c $|B - A|$\uc758 \ucd5c\uc19f\uac12\uacfc \ucd5c\ub313\uac12\uc744 \uad6c\ud574\ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 $T$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ucf00\uc774\uc2a4\uc758 \uc785\ub825\uc740 \uc138 \uc904\uc5d0 \ub098\ub204\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \uccab \uc904\uc5d0 $n$, $m$, $k$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uc5d0 Bob\uc774 \uac00\uc9c4 \uce74\ub4dc\uc5d0 \uc801\ud78c \uc218 $n$\uac1c\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \uc14b\uc9f8 \uc904\uc5d0 Alice\uac00 \uac00\uc9c4 \uce74\ub4dc\uc5d0 \uc801\ud78c \uc218 $m$\uac1c\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc815\ub2f5\uc744 \ucd5c\uc19f\uac12, \ucd5c\ub313\uac12 \uc21c\uc73c\ub85c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \uac01 \uc904\uc5d0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1 &le; T &le; 5$<\/li>\r\n\t<li>$2 &le; n, m &le; 20$<\/li>\r\n\t<li>$2 &le; k &le; \\min{(n, m, 10)}$<\/li>\r\n\t<li>$1 &le; $ \uac01 \uce74\ub4dc\uc5d0 \uc801\ud78c \uc218 $ &le; 10^8$<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>\uc608\uc81c 1-2: \ubcf8\ubb38\uc5d0\uc11c \ub2e4\ub8e8\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c 3: \uc774 \uacbd\uc6b0 Bob, Alice\uac00 \uac01\uac01 $(1, 2, 3)$\uc744 \uace8\ub77c $6$\uc810\uc529 \ub2ec\uc131\ud558\uba74 \uc810\uc218 \ucc28\uc774\uc758 \ucd5c\uc19f\uac12\uc740 $0$\uc774\ub2e4.&nbsp;Bob\uc774&nbsp;$(1, 1, 2) = 4$\uc810, Alice\uac00 $(2, 3, 3) = 8$\uc810\uc744 \ub2ec\uc131\ud558\uba74 \ucd5c\ub313\uac12\uc740 $4$\uac00 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c 4: \uc774 \uacbd\uc6b0 Bob\uc774 \ub2ec\uc131 \uac00\ub2a5\ud55c \uc810\uc218\ub294 $(2022+2021)$\uc774\uace0 Alice\uac00 \ub2ec\uc131 \uac00\ub2a5\ud55c \uc810\uc218\ub294 $(2022+2000)$\uc774\ubbc0\ub85c \ub450 \uc810\uc218 \ucc28\uc774\uc758 \ucd5c\uc19f\uac12\uacfc \ucd5c\ub313\uac12\uc740 $21$\uc774\ub2e4.<\/p>\r\n"},{"problem_id":"24432","problem_lang":"1","title":"Card Game","description":"<p>Alice and Bob love playing card games with numbers written on them.<\/p>\r\n\r\n<p>Bob has $n$ cards and Alice has $m$ cards where each card has a positive integer written on it.<\/p>\r\n\r\n<p>Each kid will choose $k$ cards out of their cards, and compute their score by summing up the numbers written on the $k$ cards - let $B$ be the score of Bob&#39;s and $A$ be the score of Alice&#39;s. Since their scores may change depending on which $k$ cards they choose, they are curious to know what the minimum and maximum values of $|B - A|$ would be.<\/p>\r\n\r\n<p>For instance, suppose that $k = 2$, Bob has $3$ cards with $[2, 3, 5]$ on them and Alice has $4$ cards with $[1, 4, 8, 9]$ written on them.<\/p>\r\n\r\n<ul>\r\n\t<li>Bob&#39;s score will be one of $5$, $7$, and $8$, if Bob were to choose two cards.<\/li>\r\n\t<li>Alice&#39;s score will be one of $5$, $9$, $10$, $12$, $13$, and $17$, if Alice were to choose two cards.<\/li>\r\n\t<li>In this case, the minimum value of $|B - A|$ is $0$ (when $B = A = 5$) and the maximum is $12$ (when $B = 5$ and $A = 17$).<\/li>\r\n<\/ul>\r\n\r\n<p>Given $k$ and the numbers written on the cards owned by the two kids, compute the minimum and maximum value of their score difference,&nbsp;$|B - A|$.<\/p>\r\n","input":"<p>The first line will contain $T$, the number of test csaes.<\/p>\r\n\r\n<p>Each test case will consist of three lines. The first line will contain $n$, $m$, and $k$, separated by whitespace. The second line will contain $n$ numbers separated by whitespace, describing Bob&#39;s $n$ cards. The third line will contain $m$ numbers separated by whitespace, describing Alice&#39;s $m$ cards.<\/p>\r\n","output":"<p>For each test case, output the minimum and maximum score differences, separated by whitespace, in each line.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1 &le; T &le; 5$<\/li>\r\n\t<li>$2 &le; n, m &le; 20$<\/li>\r\n\t<li>$2 &le; k &le; \\min{(n, m, 10)}$<\/li>\r\n\t<li>$1 &le; $ Number on each card $ &le; 10^8$<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>Cases 1-2: Discussed in the problem statement.<\/p>\r\n\r\n<p>Case 3: Bob and Alice can each choose $(1, 2, 3)$ to score $6$, which leads to the minimum score difference of $0$. If Bob chooses $(1, 1, 2) =$ score of $4$ and Alice chooses $(2, 3, 3) =$ score of $8$, then the maximum score difference would be $4$.<\/p>\r\n\r\n<p>Case 4: Bob can only score $(2022+2021)$ and Alice can only score $(2022+2000)$, where both the minimum and maximum of score difference are $21$.<\/p>\r\n"}]

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