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문제

람세스 2세가 전투에서 승리를 거두고 귀환했다. 그는 승리를 기리기 위해 웅장한 정원을 조성하기로 결심했다. 그래서 궁궐이 있는 Lubrr에서부터 시작해 Karnak 신전에 이르는 긴 길을 따라 식물을 일렬로 쭉 심을 예정이다. 심는 식물은 연꽃(L)과 파피루스(P) 이렇게 단 두 종류이다. 이들은 각각 이집트 북부와 남부의 상징이기 때문이다.

정원에는 그런 식으로 N개의 식물을 심는데, 종류별 식물 배치에 균형이 있어야 한다. 정원 내부의 어떤 연속적인 구간이라도 연꽃과 파피루스의 개수 차이가 2를 넘어서는 안 된다.

람세스가 세우고자 하는 정원은 L 아니면 P로 이루어진 문자열로 나타낼 수 있다. 예를 들어 N=5인 경우 위에서 제시한 균형을 갖춘 정원은 14가지가 있을 수 있다. (LLPLP, LLPPL, LPLLP, LPLPL, LPLPP, LPPLL, LPPLP, PLLPL, PLLPP, PLPLL, PLPLP, PLPPL, PPLLP, PPLPL)

그리고 특정 길이에 대해 균형을 갖춘 정원 식물 배치를 나타내는 문자열들은 알파벳 오름차순으로 나열하여 1부터 번호를 매길 수 있다. 가령 N=5의 경우, 12번에 해당하는 정원 문자열은 PLPPL이다.

길이가 N인 균형 잡힌 정원을 나타내는 어떤 문자열을 입력 받아 이것이 그 길이에 해당하는 전체 균형 잡힌 정원 문자열 중 오름차순으로 몇째 순서에 해당하는지 서열을 구하고, 이 값을 어떤 정수 M으로 나눈 나머지를 출력하는 프로그램을 작성하시오.

이 M이라는 수는 문제 풀이를 더 쉽게 해 주기 위해 있는 것으로, 다른 의미는 없음을 밝힌다.

입력

첫째 줄에는 심을 식물의 수 N이 주어진다. (1 ≤ N ≤ 1,000,000)

둘째 줄에는 정수 M이 주어진다. (7 ≤ M ≤ 10,000,000)

셋째 줄에는 길이가 N이며, L(연꽃)과 P(파피루스)로 이루어진 균형 잡힌 정원을 나타내는 문자열이 주어진다.

출력

0 이상 M 미만의 정수 하나를 출력한다.

입력에서 주어진 정원 문자열의 오름차순 서열을 M으로 나눈 나머지의 값이다.

예제 입력 1

5
7
PLPPL

예제 출력 1

5

예제 입력 2

12
10000
LPLLPLPPLPLL

예제 출력 2

39

힌트

예제 입력에서 PLPPL은 사실 12번째에 있는 정원 배열이다. 그래서 12를 7로 나눈 나머지인 5를 정답으로 한다.

[{"problem_id":"5470","problem_lang":"0","title":"\uade0\ud615\uc7a1\ud78c \uc9c1\uc120\ud615 \uc815\uc6d0","description":"<p>\ub78c\uc138\uc2a4 2\uc138\uac00 \uc804\ud22c\uc5d0\uc11c \uc2b9\ub9ac\ub97c \uac70\ub450\uace0 \uadc0\ud658\ud588\ub2e4. \uadf8\ub294 \uc2b9\ub9ac\ub97c \uae30\ub9ac\uae30 \uc704\ud574 \uc6c5\uc7a5\ud55c \uc815\uc6d0\uc744 \uc870\uc131\ud558\uae30\ub85c \uacb0\uc2ec\ud588\ub2e4. \uadf8\ub798\uc11c \uad81\uad90\uc774 \uc788\ub294 Lubrr\uc5d0\uc11c\ubd80\ud130 \uc2dc\uc791\ud574 Karnak \uc2e0\uc804\uc5d0 \uc774\ub974\ub294 \uae34 \uae38\uc744 \ub530\ub77c \uc2dd\ubb3c\uc744 \uc77c\ub82c\ub85c \ucb49 \uc2ec\uc744 \uc608\uc815\uc774\ub2e4. \uc2ec\ub294 \uc2dd\ubb3c\uc740 \uc5f0\uaf43(L)\uacfc \ud30c\ud53c\ub8e8\uc2a4(P) \uc774\ub807\uac8c \ub2e8 \ub450 \uc885\ub958\uc774\ub2e4. \uc774\ub4e4\uc740 \uac01\uac01 \uc774\uc9d1\ud2b8 \ubd81\ubd80\uc640 \ub0a8\ubd80\uc758 \uc0c1\uc9d5\uc774\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc815\uc6d0\uc5d0\ub294 \uadf8\ub7f0 \uc2dd\uc73c\ub85c N\uac1c\uc758 \uc2dd\ubb3c\uc744 \uc2ec\ub294\ub370, \uc885\ub958\ubcc4 \uc2dd\ubb3c \ubc30\uce58\uc5d0 \uade0\ud615\uc774 \uc788\uc5b4\uc57c \ud55c\ub2e4. \uc815\uc6d0 \ub0b4\ubd80\uc758 \uc5b4\ub5a4 \uc5f0\uc18d\uc801\uc778&nbsp;\uad6c\uac04\uc774\ub77c\ub3c4 \uc5f0\uaf43\uacfc \ud30c\ud53c\ub8e8\uc2a4\uc758 \uac1c\uc218 \ucc28\uc774\uac00 2\ub97c \ub118\uc5b4\uc11c\ub294 \uc548 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub78c\uc138\uc2a4\uac00 \uc138\uc6b0\uace0\uc790 \ud558\ub294 \uc815\uc6d0\uc740 L \uc544\ub2c8\uba74 P\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubb38\uc790\uc5f4\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4 N=5\uc778 \uacbd\uc6b0 \uc704\uc5d0\uc11c \uc81c\uc2dc\ud55c \uade0\ud615\uc744 \uac16\ucd98 \uc815\uc6d0\uc740 14\uac00\uc9c0\uac00 \uc788\uc744 \uc218 \uc788\ub2e4. (LLPLP, LLPPL, LPLLP, LPLPL, LPLPP, LPPLL, LPPLP, PLLPL, PLLPP, PLPLL, PLPLP, PLPPL, PPLLP, PPLPL)<\/p>\r\n\r\n<p>\uadf8\ub9ac\uace0 \ud2b9\uc815 \uae38\uc774\uc5d0 \ub300\ud574 \uade0\ud615\uc744 \uac16\ucd98 \uc815\uc6d0 \uc2dd\ubb3c \ubc30\uce58\ub97c \ub098\ud0c0\ub0b4\ub294 \ubb38\uc790\uc5f4\ub4e4\uc740 \uc54c\ud30c\ubcb3 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \ub098\uc5f4\ud558\uc5ec 1\ubd80\ud130 \ubc88\ud638\ub97c \ub9e4\uae38 \uc218 \uc788\ub2e4. \uac00\ub839 N=5\uc758 \uacbd\uc6b0, 12\ubc88\uc5d0 \ud574\ub2f9\ud558\ub294 \uc815\uc6d0 \ubb38\uc790\uc5f4\uc740 PLPPL\uc774\ub2e4.<\/p>\r\n\r\n<p>\uae38\uc774\uac00 N\uc778 \uade0\ud615 \uc7a1\ud78c \uc815\uc6d0\uc744 \ub098\ud0c0\ub0b4\ub294 \uc5b4\ub5a4 \ubb38\uc790\uc5f4\uc744 \uc785\ub825 \ubc1b\uc544 \uc774\uac83\uc774 \uadf8 \uae38\uc774\uc5d0 \ud574\ub2f9\ud558\ub294 \uc804\uccb4 \uade0\ud615 \uc7a1\ud78c \uc815\uc6d0 \ubb38\uc790\uc5f4 \uc911 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uba87\uc9f8 \uc21c\uc11c\uc5d0 \ud574\ub2f9\ud558\ub294\uc9c0 \uc11c\uc5f4\uc744 \uad6c\ud558\uace0, \uc774 \uac12\uc744 \uc5b4\ub5a4 \uc815\uc218 M\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc774 M\uc774\ub77c\ub294 \uc218\ub294 \ubb38\uc81c \ud480\uc774\ub97c \ub354 \uc27d\uac8c \ud574 \uc8fc\uae30 \uc704\ud574 \uc788\ub294 \uac83\uc73c\ub85c, \ub2e4\ub978 \uc758\ubbf8\ub294 \uc5c6\uc74c\uc744 \ubc1d\ud78c\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8&nbsp;\uc904\uc5d0\ub294 \uc2ec\uc744 \uc2dd\ubb3c\uc758 \uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;(1&nbsp;&le; N&nbsp;&le; 1,000,000)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 \uc815\uc218 M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;(7 &le; M &le; 10,000,000)<\/p>\r\n\r\n<p>\uc14b\uc9f8 \uc904\uc5d0\ub294 \uae38\uc774\uac00 N\uc774\uba70, L(\uc5f0\uaf43)\uacfc P(\ud30c\ud53c\ub8e8\uc2a4)\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uade0\ud615 \uc7a1\ud78c \uc815\uc6d0\uc744 \ub098\ud0c0\ub0b4\ub294 \ubb38\uc790\uc5f4\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>0 \uc774\uc0c1 M \ubbf8\ub9cc\uc758 \uc815\uc218 \ud558\ub098\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc5d0\uc11c&nbsp;\uc8fc\uc5b4\uc9c4&nbsp;\uc815\uc6d0 \ubb38\uc790\uc5f4\uc758 \uc624\ub984\ucc28\uc21c \uc11c\uc5f4\uc744 M\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\uc758 \uac12\uc774\ub2e4.<\/p>\r\n","hint":"<p>\uc608\uc81c \uc785\ub825\uc5d0\uc11c PLPPL\uc740 \uc0ac\uc2e4 12\ubc88\uc9f8\uc5d0 \uc788\ub294 \uc815\uc6d0 \ubc30\uc5f4\uc774\ub2e4. \uadf8\ub798\uc11c 12\ub97c 7\ub85c \ub098\ub208 \ub098\uba38\uc9c0\uc778 5\ub97c \uc815\ub2f5\uc73c\ub85c \ud55c\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5470","problem_lang":"1","title":"Linear Garden","description":"<p>Ramesses II has just returned victorious from battle. To commemorate his victory, he has decided to build a majestic garden. The garden will contain a long line of plants that will run all the way from his palace at Luxor to the temple of Karnak. It will consist only of lotus plants and papyrus plants, since they symbolize Upper and Lower Egypt respectively. &nbsp;<\/p>\r\n\r\n<p>The garden must contain exactly N plants. Also, it must be balanced: in any contiguous section of the garden, the numbers of lotus and papyrus plants must not differ by more than 2.<\/p>\r\n\r\n<p>A garden can be represented as a string of letters &lsquo;L&rsquo; (lotus) and &lsquo;P&rsquo; (papyrus). For example, for N=5 there are 14 possible balanced gardens. In alphabetical order, these are: LLPLP, LLPPL, LPLLP, LPLPL, LPLPP, LPPLL, LPPLP, PLLPL, PLLPP, PLPLL, PLPLP, PLPPL, PPLLP, and PPLPL. The possible balanced gardens of a certain length can be ordered alphabetically, and then numbered<\/p>\r\n\r\n<p>starting from 1. For example, for N=5, garden number 12 is the garden PLPPL.&nbsp;<br \/>\r\nWrite a program that, given the number of plants N and a string that represents a balanced garden, calculates the number assigned to this garden modulo some given integer M.<\/p>\r\n\r\n<p>Note that for solving the task, the value of M has no importance other than simplifying computations.<\/p>\r\n","input":"<p>Your program must read from the standard input the following data:<\/p>\r\n\r\n<ul>\r\n\t<li>Line 1 contains the integer N, the number of plants in the garden. (1 &le; N &le; 1,000,000)<\/li>\r\n\t<li>Line 2 contains the integer M. (7 &le; M &le; 10,000,000)<\/li>\r\n\t<li>Line 3 contains a string of N characters &lsquo;L&rsquo; (lotus) or &lsquo;P&rsquo; (papyrus) that represents a balanced garden.<\/li>\r\n<\/ul>\r\n","output":"<p>Your program must write to the standard output a single line containing one integer between 0 and M\u20101 (inclusive), the number assigned to the garden described in the input, modulo M.<\/p>\r\n","hint":"<p>The actual number assigned to PLPPL is 12. So, the output is 12 modulo 7, which is 5.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > International Olympiad in Informatics > IOI 2008 4번