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문제

본 조비 2013 투어를 기획하는 현우는 표를 복권처럼 팔기로 결정했다. 규칙은 매우 간단하다. 팬은 온라인으로 표를 구매하고, 구매하면 고유한 예약 번호를 받게 된다. 모든 공연의 예약 번호는 0부터 예약한 순서대로 주어진다. 구매한 표가 당첨이 되면 콘서트에 갈 수 있는 것이고, 아니면 콘서트에 갈 수 없는 것이다.

현우는 당첨 표의 번호를 랜덤으로 뽑는다. 하지만 현우가 사용하는 난수 생성기는 매우 느리다. 따라서, 생성기를 호출하는 횟수를 최소로 하기 위해서, 현우는 이상하지만 공정하게 당첨표를 뽑는 방법을 만들었다.

공연의 예약이 완료되면, 현우는 예약 횟수를 M으로 두고, {0, ..., M-1}에서 랜덤 정수 Z를 하나 고른다. 이렇게 하면 생성기를 한 번만 호출해도 된다. 이제 현우는 당첨표에 직접 영향을 주는 정수 r > 0을 고른다.

Z와 r을 이용해서 당첨표를 뽑는 방법은 다음과 같다.

먼저, 예약 번호 0, ..., M-1과 Z를 길이가 n인 10진수로 바꾼다. n은 M-1의 앞에 0을 붙이지 않았을 때 그 길이이다. 길이가 n보다 작은 수는 앞에 0을 붙여 길이를 모두 같게 만든다.

a1...an이 예약 변호 A이고, z1...zn이 Z일 때, A가 당첨표가 되려면, z1...zn과 a1...an에 시작 위치가 같으면서 길이가 r 이상인 공통 부분 문자열이 존재해야 한다. 즉, 1 ≤ i ≤ n-r+1이고 zi...zi+r-1 = ai...ai+r-1인 i가 존재해야 한다. 예를 들어 Z = 56743이고 r = 3인 경우에, 06740은 당첨표이지만, 56143은 당첨이 아니다.

M, Z, r이 주어졌을 때, 당첨표의 개수를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 공연의 수 C가 주어진다. (1 ≤ C ≤ 5,000) 다음 C개 줄에 대해서, 각 공연의 M, Z, r이 주어진다. (0 < M ≤ 1018, 0 ≤ Z ≤ M-1, r ≥ 1) r은 항상 M-1의 길이보다 작거나 같다.

출력

각 공연에 대해서, 당첨표의 개수를 출력한다.

예제 입력 1

8
89 32 1
67 49 1
67 45 2
1000 23 1
1000 401 2
1000 54 2
3571 2 3
3571 976 3

예제 출력 1

18
15
1
271
19
19
13
12
[{"problem_id":"9210","problem_lang":"0","title":"\ubcf5\uad8c \ud45c","description":"<p>\ubcf8 \uc870\ube44 2013 \ud22c\uc5b4\ub97c \uae30\ud68d\ud558\ub294 \ud604\uc6b0\ub294 \ud45c\ub97c \ubcf5\uad8c\ucc98\ub7fc \ud314\uae30\ub85c \uacb0\uc815\ud588\ub2e4. \uaddc\uce59\uc740 \ub9e4\uc6b0 \uac04\ub2e8\ud558\ub2e4. \ud32c\uc740 \uc628\ub77c\uc778\uc73c\ub85c \ud45c\ub97c \uad6c\ub9e4\ud558\uace0, \uad6c\ub9e4\ud558\uba74 \uace0\uc720\ud55c \uc608\uc57d \ubc88\ud638\ub97c \ubc1b\uac8c \ub41c\ub2e4. \ubaa8\ub4e0 \uacf5\uc5f0\uc758 \uc608\uc57d \ubc88\ud638\ub294 0\ubd80\ud130 \uc608\uc57d\ud55c \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uad6c\ub9e4\ud55c \ud45c\uac00 \ub2f9\ucca8\uc774 \ub418\uba74 \ucf58\uc11c\ud2b8\uc5d0 \uac08 \uc218 \uc788\ub294 \uac83\uc774\uace0, \uc544\ub2c8\uba74 \ucf58\uc11c\ud2b8\uc5d0 \uac08 \uc218 \uc5c6\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\ud604\uc6b0\ub294 \ub2f9\ucca8 \ud45c\uc758 \ubc88\ud638\ub97c \ub79c\ub364\uc73c\ub85c \ubf51\ub294\ub2e4. \ud558\uc9c0\ub9cc \ud604\uc6b0\uac00 \uc0ac\uc6a9\ud558\ub294 \ub09c\uc218 \uc0dd\uc131\uae30\ub294 \ub9e4\uc6b0 \ub290\ub9ac\ub2e4. \ub530\ub77c\uc11c, \uc0dd\uc131\uae30\ub97c \ud638\ucd9c\ud558\ub294 \ud69f\uc218\ub97c \ucd5c\uc18c\ub85c \ud558\uae30 \uc704\ud574\uc11c, \ud604\uc6b0\ub294 \uc774\uc0c1\ud558\uc9c0\ub9cc \uacf5\uc815\ud558\uac8c \ub2f9\ucca8\ud45c\ub97c \ubf51\ub294 \ubc29\ubc95\uc744 \ub9cc\ub4e4\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\uacf5\uc5f0\uc758 \uc608\uc57d\uc774 \uc644\ub8cc\ub418\uba74, \ud604\uc6b0\ub294 \uc608\uc57d \ud69f\uc218\ub97c M\uc73c\ub85c \ub450\uace0, {0, ..., M-1}\uc5d0\uc11c \ub79c\ub364 \uc815\uc218 Z\ub97c \ud558\ub098 \uace0\ub978\ub2e4. \uc774\ub807\uac8c \ud558\uba74 \uc0dd\uc131\uae30\ub97c \ud55c \ubc88\ub9cc \ud638\ucd9c\ud574\ub3c4 \ub41c\ub2e4. \uc774\uc81c \ud604\uc6b0\ub294 \ub2f9\ucca8\ud45c\uc5d0 \uc9c1\uc811 \uc601\ud5a5\uc744 \uc8fc\ub294 \uc815\uc218 r &gt; 0\uc744 \uace0\ub978\ub2e4.<\/p>\r\n\r\n<p>Z\uc640 r\uc744 \uc774\uc6a9\ud574\uc11c \ub2f9\ucca8\ud45c\ub97c \ubf51\ub294 \ubc29\ubc95\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<p>\uba3c\uc800, \uc608\uc57d \ubc88\ud638 0, ..., M-1\uacfc Z\ub97c \uae38\uc774\uac00 n\uc778 10\uc9c4\uc218\ub85c \ubc14\uafbc\ub2e4. n\uc740 M-1\uc758 \uc55e\uc5d0 0\uc744 \ubd99\uc774\uc9c0 \uc54a\uc558\uc744 \ub54c \uadf8 \uae38\uc774\uc774\ub2e4. \uae38\uc774\uac00 n\ubcf4\ub2e4 \uc791\uc740 \uc218\ub294 \uc55e\uc5d0 0\uc744 \ubd99\uc5ec \uae38\uc774\ub97c \ubaa8\ub450 \uac19\uac8c \ub9cc\ub4e0\ub2e4.<\/p>\r\n\r\n<p>a<sub>1<\/sub>...a<sub>n<\/sub>\uc774 \uc608\uc57d \ubcc0\ud638 A\uc774\uace0, z<sub>1<\/sub>...z<sub>n<\/sub>\uc774 Z\uc77c \ub54c, A\uac00 \ub2f9\ucca8\ud45c\uac00 \ub418\ub824\uba74, z<sub>1<\/sub>...z<sub>n<\/sub>\uacfc a<sub>1<\/sub>...a<sub>n<\/sub>\uc5d0 \uc2dc\uc791 \uc704\uce58\uac00 \uac19\uc73c\uba74\uc11c \uae38\uc774\uac00 r \uc774\uc0c1\uc778 \uacf5\ud1b5 \ubd80\ubd84 \ubb38\uc790\uc5f4\uc774 \uc874\uc7ac\ud574\uc57c \ud55c\ub2e4. \uc989, 1 &le; i &le; n-r+1\uc774\uace0 z<sub>i<\/sub>...z<sub>i+r-1<\/sub> = a<sub>i<\/sub>...a<sub>i+r-1<\/sub>\uc778 i\uac00 \uc874\uc7ac\ud574\uc57c \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4 Z = 56743\uc774\uace0 r = 3\uc778 \uacbd\uc6b0\uc5d0, 06740\uc740 \ub2f9\ucca8\ud45c\uc774\uc9c0\ub9cc, 56143\uc740 \ub2f9\ucca8\uc774 \uc544\ub2c8\ub2e4.<\/p>\r\n\r\n<p>M, Z, r\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ub2f9\ucca8\ud45c\uc758 \uac1c\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uacf5\uc5f0\uc758 \uc218 C\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; C &le; 5,000) \ub2e4\uc74c C\uac1c \uc904\uc5d0 \ub300\ud574\uc11c, \uac01 \uacf5\uc5f0\uc758 M, Z, r\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &lt; M &le; 10<sup>18<\/sup>, 0 &le; Z &le; M-1, r &ge; 1) r\uc740 \ud56d\uc0c1 M-1\uc758 \uae38\uc774\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4.<\/p>\r\n","output":"<p>\uac01 \uacf5\uc5f0\uc5d0 \ub300\ud574\uc11c, \ub2f9\ucca8\ud45c\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"9210","problem_lang":"1","title":"Ticket Draw","description":"<p>The concert promoters of the Bon Jovi Tour 2013 have decided to sell tickets for the concerts in lotteries. The rules are quite simple. For every concert, fans can apply online for tickets. In response they receive unique reservation numbers. It is important that for each concert the numbers distributed online are consecutive nonnegative integers starting with 0. Unfortunately, as the organizers tried to draw reservation numbers randomly, they discovered that the pseudo random generator they used is extremely slow. To minimize the number of calls to the generator, they invented a peculiar but fair enough way to distribute tickets.<\/p>\r\n\r\n<p>As soon as the reservation for a concert is finished, the organizers ascertain the number of submissions M and draw one random integer Z from {0, ... M-1} (remember, fans get integers from 0 to M-1). Integer Z is the only object the organizers have to draw randomly! Finally, to complete the selection rules the organizers determine an integer r &gt; 0 which has a direct impact on the number of selected tickets.<\/p>\r\n\r\n<p>Now, using Z and r, tickets are selected deterministically as follows. For the reservation numbers 0, ..., M-1 and the number Z, their decimal representations of length n are considered, where n is the length of the representation of M-1 without leading zeros. Thus, the decimal representations of the remaining numbers are padded on the left with leading zeros, if needed. If z<sub>1<\/sub> ... z<sub>n<\/sub> denotes such a representation for Z, then the holder of a number a1 ... an gets the ticket if and only if the strings z<sub>1<\/sub> ... z<sub>n<\/sub> and a<sub>1<\/sub> ... a<sub>n<\/sub> have a common contiguous substring of length r or more which starts at the same position. Speaking formally, he or she gets the ticket if there exists an index i, with 1 &le; i &le; n-r+1, such that z<sub>i<\/sub> ... z<sub>i+r-1<\/sub> = a<sub>i<\/sub> ... a<sub>i+r-1<\/sub>. For example, if Z = 56743 and r = 3 then a fan with a reservation number 06740 gets a ticket, but a fan having 56143 does not.<\/p>\r\n\r\n<p>Your task is to help the organizers to estimate, for given numbers M, Z and r, the exact number of tickets selected in such a way<\/p>\r\n","input":"<p>The first line contains the number of concerts C, with 1 &le; C &le; 5000. Then follow C lines, each containing three integers M, Z, and r, with 0 &lt; M &le; 10<sup>18<\/sup>, 0 &le; Z &le; M-1 and r &ge; 1. You may safely assume that r is smaller or equal to the length of the decimal representation of M-1.<\/p>\r\n","output":"<p>For each concert, print one line containing the number of tickets selected during the ticket draw.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Europe > Northwestern European Regional Contest > German Collegiate Programming Contest > GCPC 2013 I번

  • 문제를 번역한 사람: baekjoon
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