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문제

Albert는 최근 (2진수) XOR 연산과 자료구조에 흠뻑 빠져있다.

Albert는 XOR에 관련된 여러 가지 연산을 효율적으로 할 수 있는 자료 구조를 만들고 싶다. 

처음에는 n개의 정수를 포함한 집합 S0을 이용하여 자료 구조를 초기화 하며, 그 이후 q개의 연산을 수행하여 옳은 답을 출력해야한다.

각 연산은 아래 다섯 가지 중 하나이며, 일부 연산은 자료 구조에 저장된 정수 집합에 새로운 정수를 추가하거나 정수를 지우기도 한다 (따라서 그 이후의 연산은 영향을 받게 된다).

  1. find_min(v): 현재 자료 구조에 저장된 정수 집합이 S라면, (v XOR s) 값이 최소가 되는 S의 원소 s를 찾아 (v XOR s) 값을 출력한다. S는 변경되지 않는다.
  2. find_max(v): 현재 자료 구조에 저장된 정수 집합이 S라면, (v XOR s) 값이 최대가 되는 S의 원소 s를 찾아 (v XOR s) 값을 출력한다. S는 변경되지 않는다.
  3. add(v): 현재 자료 구조에 저장된 정수 집합 S에 v를 추가한다. 추가한 후, S에 저장된 고유한 정수의 개수를 출력한다.
  4. remove_min(): 현재 자료 구조에 저장된 정수 집합 S의 원소 중 가장 작은 수를 출력한 후, 이를 삭제한다. 만약 가장 작은 수가 여럿이라면 모두 삭제한다.
  5. remove_max(): 현재 자료 구조에 저장된 정수 집합 S의 원소 중 가장 큰 수를 출력한 후, 이를 삭제한다. 만약 가장 큰 수가 여럿이라면 모두 삭제한다.

예를 들어, S0 = {1,1, 3, 3} 이고 아래와 같은 순서로 총 q = 7개의 연산을 적용한다고 해보자.

  1. find_min(2): (1 XOR 2) = 3 이고 (2 XOR 3) = 1 이므로 1을 출력해야한다. 연산 적용 후, S는 바뀌지 않으므로 S = {1, 1, 3, 3} 이다.
  2. find_max(2): (1 XOR 2) = 3 이고 (2 XOR 3) = 1 이므로 3을 출력해야한다. 연산 적용 후, S는 바뀌지 않으므로 S = {1, 1, 3, 3} 이다.
  3. add(2): S에 새로운 원소를 추가하여 S = {1, 1, 2, 3, 3}이 된다. 중복을 제외하면 총 3개의 고유한 정수가 있으므로 3을 출력한다.
  4. remove_min(): S의 원소 중 가장 작은 수는 1이므로 1을 출력하고, 모두 삭제한다. 연산 적용 후, S = {2, 3, 3} 이다.
  5. remove_max(): S의 원소 중 가장 큰 수는 3이므로 3을 출력하고, 모두 삭제한다. 연산 적용 후, S = {2} 이다.
  6. find_min(2): (2 XOR 2) = 0 이므로 0을 출력해야한다.
  7. find_max(2): (2 XOR 2) = 0 이므로 0을 출력해야한다.

위의 예제의 경우, 올바른 결과는 (연산 적용 순서대로) [1, 3, 3, 1, 3, 0, 0]이 된다.

입력으로 n, S0, q, 그리고 q개의 연산을 받아 총 q개의 정수 (각 연산을 적용한 후 얻은 결과)를 출력하는 프로그램을 작성하시오.

입력

첫 줄에 테스트 케이스의 수 T가 주어진다.

각 테스트 케이스의 첫 줄에는 n과 q가 공백으로 구분 되어 주어진다.

둘째 줄에는 집합 S0에 포함된 n개의 정수가 공백으로 주어진다.

다음 q줄에 걸쳐 각 줄에 하나의 연산이 주어진다.

각 줄에는 1개 혹은 2개의 정수가 (공백으로 구분되어) 주어지는데, 첫 수는 연산의 종류를 나타내며 {1, 2, 3, 4, 5} 중 하나이다.

문제 본문에 설명된바와 같이, 1은 find_min, 2는 find_max, 3은 add, 4는 remove_min, 그리고 5는 remove_max 연산을 나타낸다.

연산 1-3의 경우에만 같은 줄에 두 번째 정수 "v"가 주어진다.

출력

각 연산을 적용한 후 자료 구조가 출력해야하는 올바른 값을 한 줄에 하나씩 출력한다.

제한

  • 1 ≤ T ≤ 10
  • 1 ≤ n, q ≤ 50,000
  • 연산과 함께 주어지는 모든 값 v에 대해 0 ≤ v < 2^25
  • S0에 주어진 모든 원소 s에 대해 0 ≤ s < 2^25
  • 모든 연산에 대하여, 각 연산을 처리하기 전이나 후에 S의 원소가 없는 경우는 입력으로 주어지지 않는다.

예제 입력 1

3
4 7
1 1 3 3
1 2
2 2
3 2
4
5
1 2
2 2
10 11
1 3 5 7 9 2 4 6 8 10
1 6
1 8
2 6
2 8
3 10
4
5
1 2
1 17
2 2
2 17
5 11
2 5 8 13 17
1 6
1 8
2 6
2 8
3 10
4
5
1 2
1 17
2 2
2 17

예제 출력 1

1
3
3
1
3
0
0
0
0
15
15
10
1
10
0
18
11
25
3
0
23
25
6
2
17
7
20
15
28

케이스 1: 본문에서 사용한 예제이다.

케이스 2: 추가 설명 없음.

케이스 3:

연산 시작 전: S = {2, 5, 8, 13, 17}

  1. find_min(6): (6 XOR 5) = 3 
  2. find_min(8):  (8 XOR 8) = 0
  3. find_max(6): (6 XOR 17) = 23
  4. find_max(8): (8 XOR 17) = 25
  5. add(10): S = {2, 5, 8, 10, 13, 17} (6개의 고유한 정수)
  6. remove_min(): S = {5, 8, 10, 13, 17} (2를 삭제함)
  7. remove_max(): S = {5, 8, 10, 13} (17을 삭제함)
  8. find_min(2): (2 XOR 5) = 7
  9. find_min(17): (17 XOR 5) = 20
  10. find_max(2): (2 XOR 13) = 15
  11. find_max(17): (17 XOR 13) = 28
[{"problem_id":"20919","problem_lang":"0","title":"XOR \uc790\ub8cc\uad6c\uc870","description":"<p>Albert\ub294 \ucd5c\uadfc (2\uc9c4\uc218) XOR \uc5f0\uc0b0\uacfc \uc790\ub8cc\uad6c\uc870\uc5d0 \ud760\ubed1 \ube60\uc838\uc788\ub2e4.<\/p>\r\n\r\n<p>Albert\ub294 XOR\uc5d0 \uad00\ub828\ub41c \uc5ec\ub7ec \uac00\uc9c0 \uc5f0\uc0b0\uc744 \ud6a8\uc728\uc801\uc73c\ub85c \ud560 \uc218 \uc788\ub294 \uc790\ub8cc \uad6c\uc870\ub97c \ub9cc\ub4e4\uace0 \uc2f6\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ucc98\uc74c\uc5d0\ub294 n\uac1c\uc758 \uc815\uc218\ub97c \ud3ec\ud568\ud55c \uc9d1\ud569 S0\uc744 \uc774\uc6a9\ud558\uc5ec \uc790\ub8cc \uad6c\uc870\ub97c \ucd08\uae30\ud654 \ud558\uba70, \uadf8 \uc774\ud6c4 q\uac1c\uc758 \uc5f0\uc0b0\uc744 \uc218\ud589\ud558\uc5ec \uc633\uc740 \ub2f5\uc744 \ucd9c\ub825\ud574\uc57c\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac01 \uc5f0\uc0b0\uc740 \uc544\ub798 \ub2e4\uc12f \uac00\uc9c0 \uc911 \ud558\ub098\uc774\uba70, \uc77c\ubd80 \uc5f0\uc0b0\uc740 \uc790\ub8cc \uad6c\uc870\uc5d0 \uc800\uc7a5\ub41c \uc815\uc218 \uc9d1\ud569\uc5d0 \uc0c8\ub85c\uc6b4 \uc815\uc218\ub97c \ucd94\uac00\ud558\uac70\ub098 \uc815\uc218\ub97c \uc9c0\uc6b0\uae30\ub3c4 \ud55c\ub2e4 (\ub530\ub77c\uc11c \uadf8 \uc774\ud6c4\uc758 \uc5f0\uc0b0\uc740 \uc601\ud5a5\uc744 \ubc1b\uac8c \ub41c\ub2e4).<\/p>\r\n\r\n<ol>\r\n\t<li>find_min(v): \ud604\uc7ac \uc790\ub8cc \uad6c\uc870\uc5d0 \uc800\uc7a5\ub41c \uc815\uc218 \uc9d1\ud569\uc774 S\ub77c\uba74, (v XOR s) \uac12\uc774 \ucd5c\uc18c\uac00 \ub418\ub294 S\uc758 \uc6d0\uc18c&nbsp;s\ub97c \ucc3e\uc544 (v XOR s) \uac12\uc744 \ucd9c\ub825\ud55c\ub2e4. S\ub294 \ubcc0\uacbd\ub418\uc9c0 \uc54a\ub294\ub2e4.<\/li>\r\n\t<li>find_max(v): \ud604\uc7ac \uc790\ub8cc \uad6c\uc870\uc5d0 \uc800\uc7a5\ub41c \uc815\uc218 \uc9d1\ud569\uc774 S\ub77c\uba74, (v XOR s) \uac12\uc774 \ucd5c\ub300\uac00&nbsp;\ub418\ub294 S\uc758 \uc6d0\uc18c&nbsp;s\ub97c \ucc3e\uc544 (v XOR s) \uac12\uc744 \ucd9c\ub825\ud55c\ub2e4. S\ub294 \ubcc0\uacbd\ub418\uc9c0 \uc54a\ub294\ub2e4.<\/li>\r\n\t<li>add(v): \ud604\uc7ac \uc790\ub8cc \uad6c\uc870\uc5d0 \uc800\uc7a5\ub41c \uc815\uc218 \uc9d1\ud569 S\uc5d0 v\ub97c \ucd94\uac00\ud55c\ub2e4. \ucd94\uac00\ud55c \ud6c4, S\uc5d0 \uc800\uc7a5\ub41c \uace0\uc720\ud55c \uc815\uc218\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/li>\r\n\t<li>remove_min(): \ud604\uc7ac \uc790\ub8cc \uad6c\uc870\uc5d0 \uc800\uc7a5\ub41c \uc815\uc218 \uc9d1\ud569 S\uc758 \uc6d0\uc18c \uc911 \uac00\uc7a5 \uc791\uc740 \uc218\ub97c \ucd9c\ub825\ud55c \ud6c4, \uc774\ub97c \uc0ad\uc81c\ud55c\ub2e4. \ub9cc\uc57d \uac00\uc7a5 \uc791\uc740 \uc218\uac00 \uc5ec\ub7ff\uc774\ub77c\uba74 \ubaa8\ub450 \uc0ad\uc81c\ud55c\ub2e4.<\/li>\r\n\t<li>remove_max(): \ud604\uc7ac \uc790\ub8cc \uad6c\uc870\uc5d0 \uc800\uc7a5\ub41c \uc815\uc218 \uc9d1\ud569 S\uc758 \uc6d0\uc18c \uc911 \uac00\uc7a5 \ud070&nbsp;\uc218\ub97c \ucd9c\ub825\ud55c \ud6c4, \uc774\ub97c \uc0ad\uc81c\ud55c\ub2e4. \ub9cc\uc57d \uac00\uc7a5 \ud070 \uc218\uac00 \uc5ec\ub7ff\uc774\ub77c\uba74 \ubaa8\ub450 \uc0ad\uc81c\ud55c\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, S0 = {1,1, 3, 3} \uc774\uace0 \uc544\ub798\uc640 \uac19\uc740 \uc21c\uc11c\ub85c \ucd1d q = 7\uac1c\uc758 \uc5f0\uc0b0\uc744 \uc801\uc6a9\ud55c\ub2e4\uace0 \ud574\ubcf4\uc790.<\/p>\r\n\r\n<ol>\r\n\t<li>find_min(2): (1 XOR 2) = 3 \uc774\uace0 (2 XOR 3) = 1 \uc774\ubbc0\ub85c 1\uc744 \ucd9c\ub825\ud574\uc57c\ud55c\ub2e4. \uc5f0\uc0b0 \uc801\uc6a9 \ud6c4, S\ub294 \ubc14\ub00c\uc9c0 \uc54a\uc73c\ubbc0\ub85c S = {1, 1, 3, 3} \uc774\ub2e4.<\/li>\r\n\t<li>find_max(2): (1 XOR 2) = 3 \uc774\uace0 (2 XOR 3) = 1 \uc774\ubbc0\ub85c 3\uc744 \ucd9c\ub825\ud574\uc57c\ud55c\ub2e4. \uc5f0\uc0b0 \uc801\uc6a9 \ud6c4, S\ub294 \ubc14\ub00c\uc9c0 \uc54a\uc73c\ubbc0\ub85c S = {1, 1, 3, 3} \uc774\ub2e4.<\/li>\r\n\t<li>add(2): S\uc5d0 \uc0c8\ub85c\uc6b4 \uc6d0\uc18c\ub97c \ucd94\uac00\ud558\uc5ec S = {1, 1, 2, 3, 3}\uc774 \ub41c\ub2e4. \uc911\ubcf5\uc744 \uc81c\uc678\ud558\uba74 \ucd1d 3\uac1c\uc758 \uace0\uc720\ud55c \uc815\uc218\uac00 \uc788\uc73c\ubbc0\ub85c 3\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/li>\r\n\t<li>remove_min(): S\uc758 \uc6d0\uc18c \uc911 \uac00\uc7a5 \uc791\uc740 \uc218\ub294 1\uc774\ubbc0\ub85c 1\uc744 \ucd9c\ub825\ud558\uace0, \ubaa8\ub450 \uc0ad\uc81c\ud55c\ub2e4. \uc5f0\uc0b0 \uc801\uc6a9 \ud6c4, S = {2, 3, 3} \uc774\ub2e4.<\/li>\r\n\t<li>remove_max(): S\uc758 \uc6d0\uc18c \uc911 \uac00\uc7a5 \ud070 \uc218\ub294 3\uc774\ubbc0\ub85c 3\uc744 \ucd9c\ub825\ud558\uace0, \ubaa8\ub450 \uc0ad\uc81c\ud55c\ub2e4. \uc5f0\uc0b0 \uc801\uc6a9 \ud6c4, S = {2} \uc774\ub2e4.<\/li>\r\n\t<li>find_min(2): (2 XOR 2) = 0 \uc774\ubbc0\ub85c 0\uc744 \ucd9c\ub825\ud574\uc57c\ud55c\ub2e4.<\/li>\r\n\t<li>find_max(2): (2 XOR 2) = 0 \uc774\ubbc0\ub85c 0\uc744 \ucd9c\ub825\ud574\uc57c\ud55c\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc704\uc758 \uc608\uc81c\uc758 \uacbd\uc6b0, \uc62c\ubc14\ub978 \uacb0\uacfc\ub294 (\uc5f0\uc0b0 \uc801\uc6a9 \uc21c\uc11c\ub300\ub85c) [1, 3, 3, 1, 3, 0, 0]\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc73c\ub85c n, S0, q, \uadf8\ub9ac\uace0 q\uac1c\uc758 \uc5f0\uc0b0\uc744 \ubc1b\uc544 \ucd1d q\uac1c\uc758 \uc815\uc218 (\uac01 \uc5f0\uc0b0\uc744 \uc801\uc6a9\ud55c \ud6c4 \uc5bb\uc740 \uacb0\uacfc)\ub97c \ucd9c\ub825\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/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 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab \uc904\uc5d0\ub294 n\uacfc q\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84 \ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 \uc9d1\ud569 S0\uc5d0 \ud3ec\ud568\ub41c&nbsp;n\uac1c\uc758 \uc815\uc218\uac00 \uacf5\ubc31\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c q\uc904\uc5d0 \uac78\uccd0 \uac01 \uc904\uc5d0 \ud558\ub098\uc758 \uc5f0\uc0b0\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \uc904\uc5d0\ub294 1\uac1c \ud639\uc740 2\uac1c\uc758 \uc815\uc218\uac00 (\uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4) \uc8fc\uc5b4\uc9c0\ub294\ub370, \uccab \uc218\ub294 \uc5f0\uc0b0\uc758 \uc885\ub958\ub97c \ub098\ud0c0\ub0b4\uba70 {1, 2, 3, 4, 5} \uc911 \ud558\ub098\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubb38\uc81c \ubcf8\ubb38\uc5d0 \uc124\uba85\ub41c\ubc14\uc640 \uac19\uc774, 1\uc740 find_min, 2\ub294 find_max, 3\uc740 add, 4\ub294 remove_min, \uadf8\ub9ac\uace0 5\ub294 remove_max \uc5f0\uc0b0\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\uc5f0\uc0b0 1-3\uc758 \uacbd\uc6b0\uc5d0\ub9cc \uac19\uc740 \uc904\uc5d0 \ub450 \ubc88\uc9f8 \uc815\uc218 &quot;v&quot;\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01&nbsp;\uc5f0\uc0b0\uc744 \uc801\uc6a9\ud55c \ud6c4 \uc790\ub8cc \uad6c\uc870\uac00 \ucd9c\ub825\ud574\uc57c\ud558\ub294 \uc62c\ubc14\ub978 \uac12\uc744 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \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; 10<\/li>\r\n\t<li>1 &le; n, q &le; 50,000<\/li>\r\n\t<li>\uc5f0\uc0b0\uacfc \ud568\uaed8 \uc8fc\uc5b4\uc9c0\ub294 \ubaa8\ub4e0 \uac12 v\uc5d0 \ub300\ud574 0 &le; v &lt; 2^25<\/li>\r\n\t<li>S0\uc5d0 \uc8fc\uc5b4\uc9c4 \ubaa8\ub4e0 \uc6d0\uc18c s\uc5d0 \ub300\ud574 0 &le; s &lt; 2^25<\/li>\r\n\t<li>\ubaa8\ub4e0 \uc5f0\uc0b0\uc5d0 \ub300\ud558\uc5ec, \uac01&nbsp;\uc5f0\uc0b0\uc744 \ucc98\ub9ac\ud558\uae30 \uc804\uc774\ub098 \ud6c4\uc5d0 S\uc758 \uc6d0\uc18c\uac00 \uc5c6\ub294 \uacbd\uc6b0\ub294 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c0\uc9c0 \uc54a\ub294\ub2e4.<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>\ucf00\uc774\uc2a4 1: \ubcf8\ubb38\uc5d0\uc11c \uc0ac\uc6a9\ud55c \uc608\uc81c\uc774\ub2e4.<\/p>\r\n\r\n<p>\ucf00\uc774\uc2a4 2: \ucd94\uac00 \uc124\uba85 \uc5c6\uc74c.<\/p>\r\n\r\n<p>\ucf00\uc774\uc2a4 3:<\/p>\r\n\r\n<p>\uc5f0\uc0b0 \uc2dc\uc791 \uc804: S = {2, 5, 8, 13, 17}<\/p>\r\n\r\n<ol>\r\n\t<li>find_min(6):&nbsp;(6 XOR 5) = 3&nbsp;<\/li>\r\n\t<li>find_min(8):&nbsp; (8 XOR 8) = 0<\/li>\r\n\t<li>find_max(6): (6 XOR 17) = 23<\/li>\r\n\t<li>find_max(8): (8 XOR 17) = 25<\/li>\r\n\t<li>add(10): S = {2, 5, 8, 10, 13, 17} (6\uac1c\uc758 \uace0\uc720\ud55c \uc815\uc218)<\/li>\r\n\t<li>remove_min(): S = {5, 8, 10, 13, 17} (2\ub97c \uc0ad\uc81c\ud568)<\/li>\r\n\t<li>remove_max(): S = {5, 8, 10, 13} (17\uc744 \uc0ad\uc81c\ud568)<\/li>\r\n\t<li>find_min(2): (2 XOR 5) = 7<\/li>\r\n\t<li>find_min(17): (17 XOR 5) = 20<\/li>\r\n\t<li>find_max(2): (2 XOR 13) = 15<\/li>\r\n\t<li>find_max(17): (17 XOR 13) = 28<\/li>\r\n<\/ol>\r\n"},{"problem_id":"20919","problem_lang":"1","title":"XOR Data Structures","description":"<p>Albert is interested in binary XOR operations and data structures.<\/p>\r\n\r\n<p>Albert wants to create a data structure that can efficiently process XOR operations.<\/p>\r\n\r\n<p>At the beginning, the data structure must be initialized with an input array S0 that contains n integers.<\/p>\r\n\r\n<p>Then, the data structure must process q operations and output correct answers.&nbsp;<\/p>\r\n\r\n<p>There are five types of operations, and some operations may modify the numbers stored within the data structure (hence, subsequent operations&#39; results will be affected by a previous operation).<\/p>\r\n\r\n<ol>\r\n\t<li>find_min(v): If S is the current set of numbers stored in the data structure, find an element s in S that minimizes&nbsp;(v XOR s), and output (v XOR s). S remains unchanged.<\/li>\r\n\t<li>find_max(v): If S is the current set of numbers stored in the data structure, find an element s in S that maximizes (v XOR s), and output (v XOR s). S remains unchanged.<\/li>\r\n\t<li>add(v): Add v to the current set S of numbers stored in the data structure. Then, output the number of unique numbers in S.<\/li>\r\n\t<li>remove_min(): Output the smallest number stored in S of the data structure, and remove it. If there are multiple smallest numbers in S, remove them all.<\/li>\r\n\t<li>remove_max(): Output the largest number stored in S of the data structure, and remove it. If there are multiple largest numbers in S, remove them all.&nbsp;<\/li>\r\n<\/ol>\r\n\r\n<p>For instance, let&nbsp;S0 = {1,1, 3, 3} (which initializes &quot;S&quot; of the data structure),&nbsp;and we process the following q = 7&nbsp;operations.<\/p>\r\n\r\n<ol>\r\n\t<li>find_min(2): Because (1 XOR 2) = 3 and (2 XOR 3) = 1, it must output 1.&nbsp;Afterwards, S remains unchanged, so S = {1, 1, 3, 3}.<\/li>\r\n\t<li>find_max(2): Because (1 XOR 2) = 3 and (2 XOR 3) = 1, it must output&nbsp;3. Afterwards, S remains unchanged, so&nbsp;S = {1, 1, 3, 3}.<\/li>\r\n\t<li>add(2): By adding a new number 2 to S, now S becomes S = {1, 1, 2, 3, 3}. There are three unique numbers in S, so it must output 3.<\/li>\r\n\t<li>remove_min(): It must output 1, the smallest number in S, and remove all 1&#39;s. Afterwards, S = {2, 3, 3}.<\/li>\r\n\t<li>remove_max(): It must output 3, the largest number in S, and remove all 3&#39;s. Afterwards, S = {2}.<\/li>\r\n\t<li>find_min(2): Because (2 XOR 2) = 0, it must output 0.<\/li>\r\n\t<li>find_max(2): Because (2 XOR 2) = 0, it must output 0.<\/li>\r\n<\/ol>\r\n\r\n<p>In the example above, the correct output (in order of the given operations) is [1, 3, 3, 1, 3, 0, 0].<\/p>\r\n\r\n<p>Given n, S0, q, and details of the q operations, output q numbers (outputs obtained by applying the given operations).<\/p>\r\n","input":"<p>The first line will contain the number of test cases, T.<\/p>\r\n\r\n<p>The first line of each test case will contain two integers, n and q, separated by a whitespace.<\/p>\r\n\r\n<p>The second line of each test case will contain n integers, separated by a whitespace.<\/p>\r\n\r\n<p>Each of the following q lines will describe one operation.<\/p>\r\n\r\n<p>Each line will contain 1 or 2 integers (separated by a whitespace) where the first integer describes the type of an operation (one of {1, 2, 3, 4, 5}).<\/p>\r\n\r\n<p>As described in the problem statement, 1 refers to&nbsp;find_min, 2 refers to&nbsp;find_max, 3 refers to&nbsp;add, 4 refers to&nbsp;remove_min, and 5 refers&nbsp;remove_max.<\/p>\r\n\r\n<p>For operations of type 1, 2, or 3, the same line will contain the second integers, &quot;v&quot;.<\/p>\r\n","output":"<p>For each operation given in the input, output the correct answer in a single line.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>1 &le; T &le; 10<\/li>\r\n\t<li>1 &le; n, q &le; 50,000<\/li>\r\n\t<li>For every number v (given along with operations), assume&nbsp;0 &le; v &lt; 2^25<\/li>\r\n\t<li>For every number s in S0, assume&nbsp;0 &le; s &lt; 2^25<\/li>\r\n\t<li>For every operation, you may assume that S is non-empty both before and after processing the operation.<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>Case 1: Explained in the problem statement.<\/p>\r\n\r\n<p>Case 2: No explanation is provided.<\/p>\r\n\r\n<p>Case 3:<\/p>\r\n\r\n<p>Before processing any operations: S = {2, 5, 8, 13, 17}<\/p>\r\n\r\n<ol>\r\n\t<li>find_min(6):&nbsp;(6 XOR 5) = 3&nbsp;<\/li>\r\n\t<li>find_min(8):&nbsp; (8 XOR 8) = 0<\/li>\r\n\t<li>find_max(6): (6 XOR 17) = 23<\/li>\r\n\t<li>find_max(8): (8 XOR 17) = 25<\/li>\r\n\t<li>add(10): S = {2, 5, 8, 10, 13, 17} (6 unique numbers)<\/li>\r\n\t<li>remove_min(): S = {5, 8, 10, 13, 17} (2 has been removed)<\/li>\r\n\t<li>remove_max(): S = {5, 8, 10, 13} (17 has been removed)<\/li>\r\n\t<li>find_min(2): (2 XOR 5) = 7<\/li>\r\n\t<li>find_min(17): (17 XOR 5) = 20<\/li>\r\n\t<li>find_max(2): (2 XOR 13) = 15<\/li>\r\n\t<li>find_max(17): (17 XOR 13) = 28<\/li>\r\n<\/ol>\r\n"}]