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문제

인간의 DNA 구조는 A, C, G, T로 이루어진 하나의 긴 문자열로 표현할 수 있다.

이 때, 몇 몇 질병은 DNA 구조를 나타낸 문자열의 어떤 연속된 부분 문자열과 관련이 있다는 것이 밝혀져 있다. 만일 DNA가 특정 문자열을 부분 문자열로 가진다면 그 질병에 걸릴 가능성이 높다는 것이다. 이러한 특정 문자열을 마커(marker)라 한다.

하지만 때때로 DNA 구조를 그대로 확인하는 것만으로는 질병과 관련된 마커를 확인할 수 없는 경우가 있다. 마커의 돌연변이 가능성 때문이다.

마커의 돌연변이는 아래와 같이 일어난다.

  • 먼저, 마커를 세 부분으로 나눈다, 이 때, 첫 부분과 세 번째 부분은 비어 있어도 된다.
  • 두 번째 부분을 뒤집는다.

예를 들어 마커가 AGGT라면 아래와 같은 여섯 가지 경우가 가능하다.

GAGT, GGAT, TGGA, AGGT, ATGG, AGTG

어떤 사람의 DNA 구조와 마커가 주어졌을 때, DNA 내에 마커가 돌연변이의 형태를 포함하여 몇 번 출현하는지 세는 프로그램을 작성하라.

단, 마커의 출현 위치는 서로 겹쳐도 된다. 예를 들어 DNA 구조가 ATGGAT이며 마커가 AGGT라면 답은 3이 된다. ATGG, TGGA, GGAT가 한 번씩 출현하기 때문이다.

입력

첫 줄에 테스트 케이스의 수 T가 주어진다.

각 테스트 케이스의 첫 줄엔 두 개의 정수 n과 m이 주어진다. 이는 각각 DNA 문자열의 길이와 마커의 길이이다. (1 ≤ n ≤ 1,000,000, 1 ≤ m ≤ 100) 두 번째 줄엔 DNA 구조가 주어진다. 마지막 줄엔 마커가 주어진다.

모든 DNA와 마커는 A,G,T,C로만 이루어진 문자열이다.

출력

각 테스트 케이스마다 주어진 DNA 구조에 마커와 그 돌연변이가 몇 번 출현하는지 하나의 정수로 출력한다.

만일 DNA 구조 내에 마커 또는 그 돌연변이가 한 번도 출현하지 않는다면 답은 0이 된다.

예제 입력 1

2
6 4
ATGGAT
AGGT
6 4
ATGGAT
AGCT

예제 출력 1

3
0

힌트

[{"problem_id":"10256","problem_lang":"0","title":"\ub3cc\uc5f0\ubcc0\uc774","description":"<p>\uc778\uac04\uc758 DNA \uad6c\uc870\ub294 A, C, G, T\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ud558\ub098\uc758 \uae34 \ubb38\uc790\uc5f4\ub85c \ud45c\ud604\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc774 \ub54c, \uba87 \uba87 \uc9c8\ubcd1\uc740 DNA \uad6c\uc870\ub97c \ub098\ud0c0\ub0b8 \ubb38\uc790\uc5f4\uc758 \uc5b4\ub5a4 \uc5f0\uc18d\ub41c \ubd80\ubd84 \ubb38\uc790\uc5f4\uacfc \uad00\ub828\uc774 \uc788\ub2e4\ub294 \uac83\uc774 \ubc1d\ud600\uc838 \uc788\ub2e4. \ub9cc\uc77c DNA\uac00 \ud2b9\uc815 \ubb38\uc790\uc5f4\uc744 \ubd80\ubd84 \ubb38\uc790\uc5f4\ub85c \uac00\uc9c4\ub2e4\uba74 \uadf8 \uc9c8\ubcd1\uc5d0 \uac78\ub9b4 \uac00\ub2a5\uc131\uc774 \ub192\ub2e4\ub294 \uac83\uc774\ub2e4. \uc774\ub7ec\ud55c \ud2b9\uc815 \ubb38\uc790\uc5f4\uc744 \ub9c8\ucee4(marker)\ub77c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud558\uc9c0\ub9cc \ub54c\ub54c\ub85c DNA \uad6c\uc870\ub97c \uadf8\ub300\ub85c \ud655\uc778\ud558\ub294 \uac83\ub9cc\uc73c\ub85c\ub294 \uc9c8\ubcd1\uacfc \uad00\ub828\ub41c \ub9c8\ucee4\ub97c \ud655\uc778\ud560 \uc218 \uc5c6\ub294 \uacbd\uc6b0\uac00 \uc788\ub2e4. \ub9c8\ucee4\uc758 \ub3cc\uc5f0\ubcc0\uc774 \uac00\ub2a5\uc131 \ub54c\ubb38\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub9c8\ucee4\uc758 \ub3cc\uc5f0\ubcc0\uc774\ub294 \uc544\ub798\uc640 \uac19\uc774 \uc77c\uc5b4\ub09c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uba3c\uc800, \ub9c8\ucee4\ub97c \uc138 \ubd80\ubd84\uc73c\ub85c \ub098\ub208\ub2e4, \uc774 \ub54c, \uccab \ubd80\ubd84\uacfc \uc138 \ubc88\uc9f8 \ubd80\ubd84\uc740 \ube44\uc5b4 \uc788\uc5b4\ub3c4 \ub41c\ub2e4.<\/li>\r\n\t<li>\ub450 \ubc88\uc9f8 \ubd80\ubd84\uc744 \ub4a4\uc9d1\ub294\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4 \ub9c8\ucee4\uac00 AGGT\ub77c\uba74 \uc544\ub798\uc640 \uac19\uc740 \uc5ec\uc12f \uac00\uc9c0 \uacbd\uc6b0\uac00 \uac00\ub2a5\ud558\ub2e4.<\/p>\r\n\r\n<p>GAGT, GGAT, TGGA, AGGT, ATGG, AGTG<\/p>\r\n\r\n<p>\uc5b4\ub5a4 \uc0ac\ub78c\uc758 DNA \uad6c\uc870\uc640 \ub9c8\ucee4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, DNA \ub0b4\uc5d0 \ub9c8\ucee4\uac00 \ub3cc\uc5f0\ubcc0\uc774\uc758 \ud615\ud0dc\ub97c \ud3ec\ud568\ud558\uc5ec \uba87 \ubc88 \ucd9c\ud604\ud558\ub294\uc9c0 \uc138\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\ub77c.<\/p>\r\n\r\n<p>\ub2e8, \ub9c8\ucee4\uc758 \ucd9c\ud604 \uc704\uce58\ub294 \uc11c\ub85c \uacb9\uccd0\ub3c4 \ub41c\ub2e4. \uc608\ub97c \ub4e4\uc5b4 DNA \uad6c\uc870\uac00 ATGGAT\uc774\uba70 \ub9c8\ucee4\uac00 AGGT\ub77c\uba74 \ub2f5\uc740 3\uc774 \ub41c\ub2e4. ATGG, TGGA, GGAT\uac00 \ud55c \ubc88\uc529 \ucd9c\ud604\ud558\uae30 \ub54c\ubb38\uc774\ub2e4.<\/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\uc5d4 \ub450 \uac1c\uc758 \uc815\uc218 n\uacfc m\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;<span style=\"line-height:1.6em\">\uc774\ub294 \uac01\uac01 DNA \ubb38\uc790\uc5f4\uc758 \uae38\uc774\uc640 \ub9c8\ucee4\uc758 \uae38\uc774\uc774\ub2e4. (1 &le; n &le; 1,000,000, 1 &le; m &le; 100)&nbsp;<\/span><span style=\"line-height:1.6em\">\ub450 \ubc88\uc9f8 \uc904\uc5d4 DNA \uad6c\uc870\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;<\/span><span style=\"line-height:1.6em\">\ub9c8\uc9c0\ub9c9 \uc904\uc5d4 \ub9c8\ucee4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/span><\/p>\r\n\r\n<p>\ubaa8\ub4e0 DNA\uc640 \ub9c8\ucee4\ub294 A,G,T,C\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc9c4 \ubb38\uc790\uc5f4\uc774\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \uc8fc\uc5b4\uc9c4 DNA \uad6c\uc870\uc5d0 \ub9c8\ucee4\uc640 \uadf8 \ub3cc\uc5f0\ubcc0\uc774\uac00 \uba87 \ubc88 \ucd9c\ud604\ud558\ub294\uc9c0 \ud558\ub098\uc758 \uc815\uc218\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc77c DNA \uad6c\uc870 \ub0b4\uc5d0 \ub9c8\ucee4 \ub610\ub294 \uadf8 \ub3cc\uc5f0\ubcc0\uc774\uac00 \ud55c \ubc88\ub3c4 \ucd9c\ud604\ud558\uc9c0 \uc54a\ub294\ub2e4\uba74 \ub2f5\uc740 0\uc774 \ub41c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"10256","problem_lang":"1","title":"Mutation","description":"<p>The human DNA sequence can be considered as a long string made up with four letters, A, G, T, and C. It is known that some diseases are related to a marker, a short substring of the DNA sequence. If your DNA contains it, then it is likely that you have a higher probability of suffering from those diseases.&nbsp;<\/p>\r\n\r\n<p>Sometimes it is not enough to find markers from your DNA sequences. Mutation can change the marker. That is, the marker can be divided into three parts and the middle one can be reversed. Note that the first or the third one can be an empty string. For example, if the marker is AGGT, considering the mutation, there can be six cases: GAGT, GGAT, TGGA, AGGT, ATGG, and AGTG.&nbsp;<\/p>\r\n\r\n<p>Given your DNA sequence and the marker, write a program which computes the number of occurrences of the marker or its mutations. For example, if your DNA sequence is ATGGAT and the marker is AGGT again, the answer is 3 as it includes ATGG, TGGA, and GGAT.&nbsp;<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with integers n and m, the length of your DNA sequence and that of the marker, respectively, where 1 &le; n &le; 1, 000, 000 and 1 &le; m &le; 100. The second line of each test case contains your DNA sequence. The third line of each test case contains the marker. All the strings are made up with four letters, A, G, T, and C.&nbsp;<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line for each test case. The line should contain an integer which is the number of occurrences of the marker and its mutated strings in your DNA sequence. If there is no such occurrence, print 0.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]