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문제

먹고또자니 <거기 누구세요> 코너에서는 "돌림판"을 돌려 상품을 얻을 수 있다. 이 돌림판은 큰 원형판이 N등분되어있는 형태이다.

N등분 된 각 부분은 0부터 9사이의 숫자가 하나씩 적혀있다. 게임이 시작되면, 임의의 M자리의 수 X와 Y(X ≤ Y)가 주어진다. (단, 이 수는 0으로 시작될 수도 있다.)
그리고 참가자는 돌림판을 힘차게 돌린다. 힘차게 돌던 돌림판이 완전히 멈추게 되는 순간, 12시 방향의 스피너가 특정 부분을 가리키게 될 것이다. 거기서부터 시계방향으로 M칸 연속되는 수를 읽으면 M자리의 수 Z를 얻을 수 있다.

이때 얻은 Z가 X ≤ Z ≤ Y를 만족한다면 게임을 승리하고 Z만원을 얻을 수 있다!

The wheel of Numbers

예를 들어, 돌림판이 N = 8 등분되어있고, 시계방향으로 읽었을 때 [3, 7, 8, 3, 1, 9, 2, 7] 과 같다고 하자. X = 200 이고 Y = 311일 경우 "숫자 2"가 적힌 부분부터 시작한다면 Z = 273 으로 X = 200 ≤ 273 ≤ 311 = Y 를 만족하여 게임을 승리한다.

돌림판의 상태와 X, Y가 주어질 때 어느 부분부터 시작하면 게임을 승리할 수 있을 지 알 수 있다. 주어진 조건에 대해서 게임을 승리할 수 있는 가지수를 계산하는 프로그램을 작성하시오.

입력

첫 번째 줄에 테스트케이스의 개수 T가 주어진다.

각 테스트케이스의 첫 줄에는 돌림판을 N등분할 정수 N (1 ≤ N ≤ 100)과 X, Y의 길이 M (1 ≤ M ≤ 9, M ≤ N) 이 주어진다. 그리고 다음 3개의 줄에 X의 각 자리수, Y의 각 자리수, 돌림판의 상태가 주어진다.

X와 Y의 각 자리수는 공백으로 구분되어 0~9사이의 숫자가 한자리씩 주어진다.

돌림판의 상태는 어느 부분부터 시계방향으로 읽었을 때 나타나는 순서대로 주어진다. 돌림판의 숫자도 0~9사이의 숫자가 공백으로 구분되어 주어진다.

출력

각 테스트케이스에 대하여 한 줄씩 정답을 출력한다.

즉, 돌림판에서 X ≤ Z ≤ Y를 만족하는 M자리의 수 Z가 몇 개가 있는 지를 출력한다. 단, 같은 수라도 시작 부분이 다르다면 다른 가지수로 센다. 예를 들어, X와 Y 사이에 있는 수가 123 밖에 없는 데 돌림판에서 2번 나온다면, 1이 아닌 2를 출력한다.

예제 입력 1

3
8 3
2 0 0
3 1 1
3 7 8 3 1 9 2 7
5 2
8 8
9 9
1 3 2 5 4
6 3
0 0 0
9 9 9
1 2 3 4 5 6

예제 출력 1

1
0
6
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(\ub2e8, \uc774 \uc218\ub294 0\uc73c\ub85c \uc2dc\uc791\ub420 \uc218\ub3c4 \uc788\ub2e4.)<br \/>\r\n\uadf8\ub9ac\uace0 \ucc38\uac00\uc790\ub294&nbsp;\ub3cc\ub9bc\ud310\uc744 \ud798\ucc28\uac8c \ub3cc\ub9b0\ub2e4. \ud798\ucc28\uac8c \ub3cc\ub358 \ub3cc\ub9bc\ud310\uc774 \uc644\uc804\ud788&nbsp;\uba48\ucd94\uac8c \ub418\ub294 \uc21c\uac04, 12\uc2dc \ubc29\ud5a5\uc758 \uc2a4\ud53c\ub108\uac00 \ud2b9\uc815 \ubd80\ubd84\uc744 \uac00\ub9ac\ud0a4\uac8c \ub420 \uac83\uc774\ub2e4.&nbsp;\uac70\uae30\uc11c\ubd80\ud130 \uc2dc\uacc4\ubc29\ud5a5\uc73c\ub85c M\uce78 \uc5f0\uc18d\ub418\ub294 \uc218\ub97c \uc77d\uc73c\uba74 M\uc790\ub9ac\uc758 \uc218 Z\ub97c \uc5bb\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc774\ub54c&nbsp;\uc5bb\uc740 Z\uac00&nbsp;X &le; Z &le; Y\ub97c \ub9cc\uc871\ud55c\ub2e4\uba74 \uac8c\uc784\uc744 \uc2b9\ub9ac\ud558\uace0 Z\ub9cc\uc6d0\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4!<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"The wheel of Numbers\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/11504\/1.png\" style=\"height:240px; width:366px\" title=\"The wheel of Numbers\" \/><\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, \ub3cc\ub9bc\ud310\uc774 N = 8 \ub4f1\ubd84\ub418\uc5b4\uc788\uace0, \uc2dc\uacc4\ubc29\ud5a5\uc73c\ub85c \uc77d\uc5c8\uc744 \ub54c [3, 7, 8, 3, 1, 9, 2, 7]&nbsp;\uacfc \uac19\ub2e4\uace0 \ud558\uc790. X = 200 \uc774\uace0 Y = 311\uc77c \uacbd\uc6b0 &quot;\uc22b\uc790 2&quot;\uac00 \uc801\ud78c \ubd80\ubd84\ubd80\ud130 \uc2dc\uc791\ud55c\ub2e4\uba74 Z = 273 \uc73c\ub85c&nbsp;X = 200 &le; 273 &le; 311 = Y \ub97c \ub9cc\uc871\ud558\uc5ec \uac8c\uc784\uc744 \uc2b9\ub9ac\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub3cc\ub9bc\ud310\uc758 \uc0c1\ud0dc\uc640 X, Y\uac00 \uc8fc\uc5b4\uc9c8 \ub54c \uc5b4\ub290 \ubd80\ubd84\ubd80\ud130 \uc2dc\uc791\ud558\uba74 \uac8c\uc784\uc744 \uc2b9\ub9ac\ud560 \uc218 \uc788\uc744 \uc9c0 \uc54c&nbsp;\uc218 \uc788\ub2e4. \uc8fc\uc5b4\uc9c4 \uc870\uac74\uc5d0 \ub300\ud574\uc11c \uac8c\uc784\uc744 \uc2b9\ub9ac\ud560 \uc218 \uc788\ub294 \uac00\uc9c0\uc218\ub97c \uacc4\uc0b0\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc758 \uac1c\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 \ub3cc\ub9bc\ud310\uc744 N\ub4f1\ubd84\ud560 \uc815\uc218&nbsp;N&nbsp;(1 &le; N &le; 100)\uacfc X, Y\uc758 \uae38\uc774 M&nbsp;(1 &le; M&nbsp;&le; 9,&nbsp;M &le; N) \uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uadf8\ub9ac\uace0&nbsp;\ub2e4\uc74c 3\uac1c\uc758 \uc904\uc5d0 X\uc758 \uac01 \uc790\ub9ac\uc218, Y\uc758 \uac01 \uc790\ub9ac\uc218, \ub3cc\ub9bc\ud310\uc758 \uc0c1\ud0dc\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>X\uc640 Y\uc758 \uac01 \uc790\ub9ac\uc218\ub294 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 0~9\uc0ac\uc774\uc758 \uc22b\uc790\uac00&nbsp;\ud55c\uc790\ub9ac\uc529 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub3cc\ub9bc\ud310\uc758 \uc0c1\ud0dc\ub294 \uc5b4\ub290 \ubd80\ubd84\ubd80\ud130 \uc2dc\uacc4\ubc29\ud5a5\uc73c\ub85c \uc77d\uc5c8\uc744 \ub54c \ub098\ud0c0\ub098\ub294 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ub3cc\ub9bc\ud310\uc758 \uc22b\uc790\ub3c4 0~9\uc0ac\uc774\uc758 \uc22b\uc790\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\uc5d0 \ub300\ud558\uc5ec \ud55c \uc904\uc529 \uc815\ub2f5\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc989, \ub3cc\ub9bc\ud310\uc5d0\uc11c&nbsp;X &le; Z &le; Y\ub97c \ub9cc\uc871\ud558\ub294 M\uc790\ub9ac\uc758 \uc218 Z\uac00 \uba87 \uac1c\uac00 \uc788\ub294 \uc9c0\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub2e8, \uac19\uc740 \uc218\ub77c\ub3c4 \uc2dc\uc791&nbsp;\ubd80\ubd84\uc774 \ub2e4\ub974\ub2e4\uba74 \ub2e4\ub978 \uac00\uc9c0\uc218\ub85c \uc13c\ub2e4.&nbsp;\uc608\ub97c \ub4e4\uc5b4, X\uc640 Y \uc0ac\uc774\uc5d0 \uc788\ub294 \uc218\uac00 123 \ubc16\uc5d0 \uc5c6\ub294 \ub370 \ub3cc\ub9bc\ud310\uc5d0\uc11c 2\ubc88 \ub098\uc628\ub2e4\uba74, 1\uc774 \uc544\ub2cc 2\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"11504","problem_lang":"1","title":"Wheel of Numbers","description":"<p>A new gambling machine called &ldquo;the wheel of numbers&rdquo; is introduced. It is made up with a large wheel, which is equally divided into n&nbsp;segments. Each segment contains a digit between 0 and 9, inclusively. Initially you are given two m-digit numbers X and Y (X &le; Y). Note that these numbers may begin with 0. Then, you shoot a ball aiming at the fast-rotating wheel. Your ball will hit one of its segments. Then, you take m&nbsp;consecutive segments clockwise from there and obtain an m-digit number Z. You win if X &le; Z &le; Y and lose otherwise.<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/11504\/1.png\" style=\"height:240px; width:366px\" \/><\/p>\r\n\r\n<p>For example, assume that the wheel is divided into n = 8 segments, and let [3, 7, 8, 3, 1, 9, 2, 7] be the numbers by picking one segment and reading numbers clockwise. If X = 200 and Y = 311, you win if your ball hits the segment with 2 as your number Z = 273 and surely X = 200 &le; 273 &le; 311 = Y.<\/p>\r\n\r\n<p>Once you are given the wheel, X and Y, you would like to know your winning probability. It can be calculated easily if you know how many times the numbers satisfying the above mentioned condition appear on the wheel. Write a program that counts the number of their occurrences.<\/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 a line containing two integers, n (1 &le; n &le; 100) and m (1 &le; m &le; 9 and m &le; n), where n is the number of segments in the wheel and m is the length of X and Y. The next line contains m digits representing X where each digit is between 0 and 9, inclusively, and separated by a space. The next line contains m digits representing Y as mentioned above. The following line contains n digits, separated by a space, obtained by reading numbers clockwise starting at some segment of the wheel. Again each digit is between 0 and 9, inclusively.<\/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 representing the number of occurrences of m-digit number Z contained in the wheel such that X &le; Z &le; Y. Note that if the same number appears more than twice, count them separately. For example, if 123 is the only number between X and Y and it appears twice on the wheel, the answer is 2, not 1.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Asia Pacific > Korea > Asia Regional - Daejeon 2015 L번