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2 초 128 MB 52 19 16 51.613%

문제

바이너리 트리는 트리 자료 구조로 각 노드가 최대 2개의 자식을 갖는다. 보통 두 자식은 왼쪽 자식과 오른쪽 자식으로 구분한다. 자식을 갖는 노드는 그 자식의 부모라고 한다.

지시 문자열은 문자열 L, R, U로만 이루여져 있는 문자열이다. L은 왼쪽, R은 오른쪽, U는 위를 의미한다.

어느날 상현이는 무한 바이너리 트리를 그리고 있었다. 이 트리의 모든 노드는 두 개의 자식을 갖으며, 모든 노드는 부모를 갖는다. 루트의 부모는 루트 그 자신이 된다. 그 다음 김숭이 보내준 지시 문자열 S을 이용해 트리를 이동하려고 한다. L은 왼쪽 자식, R은 오른쪽 자식, U는 부모로 이동하는 것을 의미한다.

김숭이 보내준 문자열 S를 이용해 트리를 이동하려고 하는 순간, 강수가 지시 문자열 T를 보내줬다. 상현이는 S를 이용해 트리를 이동한 후 그 즉시 T를 이용해 트리를 이동하려고 한다. 하지만, 상현이는 S를 이용해 이동하면 매우 지친 상태가 될 수 있기 때문에, T의 문자열 중 일부는 스킵할 수도 있다. 이 때, 이동이 끝나는 노드의 개수를 구해보자.

예를 들어, S = L, T = LU인 경우 답은 3이다. S를 이용해 이동하면 루트의 왼쪽 자식에서 이동을 마치게 되고, 이제 T를 이용하면 다음과 같은 4가지 경우가 생긴다.

  1. T의 모든 글자를 스킵하는 경우 루트의 왼쪽 자식에서 이동을 마치게 된다.
  2. L을 스킵하는 경우에는 루트에서 이동을 마치게 된다.
  3. U를 스킵하는 경우에는 루트의 왼쪽 자식의 왼쪽 자식에서 이동을 마치게 된다.
  4. L과 U를 모두 스킵하지 않는 경우에는 루트의 왼쪽 자식에서 이동을 마치게 된다.

T를 이용해 이동을 마친 후 가능한 최종 노드의 수는 3개이다.

입력

첫째 줄에 테스트 케이스의 개수 N(≤15)가 주어진다. 각 테스트 케이스는 두 개의 문자열로 이루어져 있으며, 길이는 100000을 넘지 않는다. 첫째 줄에는 문자열 S, 둘째 줄에는 문자열 T가 주어지며, 모두 L, R, U로만 이루어져 있다.

출력

각 테스트 케이스 마다 이동을 마칠 수 있는 노드의 개수를 출력한다. 답이 매우 커질 수 있기 때문에 21092013으로 나눈 나머지를 출력한다.

예제 입력 1

2
L
LU
L
L

예제 출력 1

Case 1: 3
Case 2: 2

힌트

[{"problem_id":"9596","problem_lang":"0","title":"\ubc14\uc774\ub108\ub9ac \ud2b8\ub9ac","description":"<p>\ubc14\uc774\ub108\ub9ac \ud2b8\ub9ac\ub294 \ud2b8\ub9ac \uc790\ub8cc \uad6c\uc870\ub85c \uac01 \ub178\ub4dc\uac00 \ucd5c\ub300 2\uac1c\uc758 \uc790\uc2dd\uc744 \uac16\ub294\ub2e4. \ubcf4\ud1b5 \ub450 \uc790\uc2dd\uc740 \uc67c\ucabd \uc790\uc2dd\uacfc \uc624\ub978\ucabd \uc790\uc2dd\uc73c\ub85c \uad6c\ubd84\ud55c\ub2e4. \uc790\uc2dd\uc744 \uac16\ub294 \ub178\ub4dc\ub294 \uadf8 \uc790\uc2dd\uc758 \ubd80\ubaa8\ub77c\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc9c0\uc2dc \ubb38\uc790\uc5f4\uc740 \ubb38\uc790\uc5f4 L, R, U\ub85c\ub9cc \uc774\ub8e8\uc5ec\uc838 \uc788\ub294 \ubb38\uc790\uc5f4\uc774\ub2e4. L\uc740 \uc67c\ucabd, R\uc740 \uc624\ub978\ucabd, U\ub294 \uc704\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc5b4\ub290\ub0a0 \uc0c1\ud604\uc774\ub294 \ubb34\ud55c \ubc14\uc774\ub108\ub9ac \ud2b8\ub9ac\ub97c \uadf8\ub9ac\uace0 \uc788\uc5c8\ub2e4. \uc774 \ud2b8\ub9ac\uc758 \ubaa8\ub4e0 \ub178\ub4dc\ub294 \ub450 \uac1c\uc758 \uc790\uc2dd\uc744 \uac16\uc73c\uba70, \ubaa8\ub4e0 \ub178\ub4dc\ub294 \ubd80\ubaa8\ub97c \uac16\ub294\ub2e4. \ub8e8\ud2b8\uc758 \ubd80\ubaa8\ub294 \ub8e8\ud2b8 \uadf8 \uc790\uc2e0\uc774 \ub41c\ub2e4. \uadf8 \ub2e4\uc74c \uae40\uc22d\uc774 \ubcf4\ub0b4\uc900 \uc9c0\uc2dc \ubb38\uc790\uc5f4 S\uc744 \uc774\uc6a9\ud574 \ud2b8\ub9ac\ub97c \uc774\ub3d9\ud558\ub824\uace0 \ud55c\ub2e4. L\uc740 \uc67c\ucabd \uc790\uc2dd, R\uc740 \uc624\ub978\ucabd \uc790\uc2dd, U\ub294 \ubd80\ubaa8\ub85c \uc774\ub3d9\ud558\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uae40\uc22d\uc774 \ubcf4\ub0b4\uc900 \ubb38\uc790\uc5f4 S\ub97c \uc774\uc6a9\ud574 \ud2b8\ub9ac\ub97c \uc774\ub3d9\ud558\ub824\uace0 \ud558\ub294 \uc21c\uac04, \uac15\uc218\uac00 \uc9c0\uc2dc \ubb38\uc790\uc5f4 T\ub97c \ubcf4\ub0b4\uc92c\ub2e4. \uc0c1\ud604\uc774\ub294 S\ub97c \uc774\uc6a9\ud574 \ud2b8\ub9ac\ub97c \uc774\ub3d9\ud55c \ud6c4 \uadf8 \uc989\uc2dc T\ub97c \uc774\uc6a9\ud574 \ud2b8\ub9ac\ub97c \uc774\ub3d9\ud558\ub824\uace0 \ud55c\ub2e4. \ud558\uc9c0\ub9cc, \uc0c1\ud604\uc774\ub294 S\ub97c \uc774\uc6a9\ud574 \uc774\ub3d9\ud558\uba74 \ub9e4\uc6b0 \uc9c0\uce5c \uc0c1\ud0dc\uac00 \ub420 \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0, T\uc758 \ubb38\uc790\uc5f4 \uc911 \uc77c\ubd80\ub294 \uc2a4\ud0b5\ud560 \uc218\ub3c4 \uc788\ub2e4. \uc774 \ub54c, \uc774\ub3d9\uc774 \ub05d\ub098\ub294 \ub178\ub4dc\uc758 \uac1c\uc218\ub97c \uad6c\ud574\ubcf4\uc790.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, S = L, T = LU\uc778 \uacbd\uc6b0 \ub2f5\uc740 3\uc774\ub2e4. S\ub97c \uc774\uc6a9\ud574 \uc774\ub3d9\ud558\uba74 \ub8e8\ud2b8\uc758 \uc67c\ucabd \uc790\uc2dd\uc5d0\uc11c \uc774\ub3d9\uc744 \ub9c8\uce58\uac8c \ub418\uace0, \uc774\uc81c T\ub97c \uc774\uc6a9\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc740 4\uac00\uc9c0 \uacbd\uc6b0\uac00 \uc0dd\uae34\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>T\uc758 \ubaa8\ub4e0 \uae00\uc790\ub97c \uc2a4\ud0b5\ud558\ub294 \uacbd\uc6b0 \ub8e8\ud2b8\uc758 \uc67c\ucabd \uc790\uc2dd\uc5d0\uc11c \uc774\ub3d9\uc744 \ub9c8\uce58\uac8c \ub41c\ub2e4.<\/li>\r\n\t<li>L\uc744 \uc2a4\ud0b5\ud558\ub294 \uacbd\uc6b0\uc5d0\ub294 \ub8e8\ud2b8\uc5d0\uc11c \uc774\ub3d9\uc744 \ub9c8\uce58\uac8c \ub41c\ub2e4.<\/li>\r\n\t<li>U\ub97c \uc2a4\ud0b5\ud558\ub294 \uacbd\uc6b0\uc5d0\ub294 \ub8e8\ud2b8\uc758 \uc67c\ucabd \uc790\uc2dd\uc758 \uc67c\ucabd \uc790\uc2dd\uc5d0\uc11c \uc774\ub3d9\uc744 \ub9c8\uce58\uac8c \ub41c\ub2e4.<\/li>\r\n\t<li>L\uacfc U\ub97c \ubaa8\ub450 \uc2a4\ud0b5\ud558\uc9c0 \uc54a\ub294 \uacbd\uc6b0\uc5d0\ub294 \ub8e8\ud2b8\uc758 \uc67c\ucabd \uc790\uc2dd\uc5d0\uc11c \uc774\ub3d9\uc744 \ub9c8\uce58\uac8c \ub41c\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>T\ub97c \uc774\uc6a9\ud574 \uc774\ub3d9\uc744 \ub9c8\uce5c \ud6c4 \uac00\ub2a5\ud55c \ucd5c\uc885 \ub178\ub4dc\uc758 \uc218\ub294 3\uac1c\uc774\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 N(&le;15)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ub450 \uac1c\uc758 \ubb38\uc790\uc5f4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, \uae38\uc774\ub294 100000\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4. \uccab\uc9f8 \uc904\uc5d0\ub294 \ubb38\uc790\uc5f4 S, \ub458\uc9f8 \uc904\uc5d0\ub294 \ubb38\uc790\uc5f4 T\uac00 \uc8fc\uc5b4\uc9c0\uba70, \ubaa8\ub450 L, R, U\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub9c8\ub2e4 \uc774\ub3d9\uc744 \ub9c8\uce60 \uc218 \uc788\ub294 \ub178\ub4dc\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub2f5\uc774 \ub9e4\uc6b0 \ucee4\uc9c8 \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0 21092013\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9596","problem_lang":"1","title":"Binary Tree","description":"<p>Binary Tree is a tree data structure where each node has at most two children, usually they are distinguished as left and right child. And the node having the children are called parent of those children.<\/p>\r\n\r\n<p>An instruction string is a string consisting of the letters L, R and U. L stands for Left, R for Right and U for Up. Meaning of these will be clear shortly.<\/p>\r\n\r\n<p>One day I have drawn an in\ufb01nitely large Binary Tree. In this tree each node has exactly two children (left child and right child) and each of them has a parent. For this problem, we will consider the parent of the root is root itself. I put a pen in the root and follow the instruction string S. That is, we look at the \ufb01rst character if it says L we go to left child, if it says R we go to right child and if it says U then to the parent. If we receive a U instruction at root we just end up at root since we assumed parent of the root is root itself.<\/p>\r\n\r\n<p>Now we have another instruction string T. Starting from the node where we are after following the instruction string S, we will follow the instruction string T. But this time, if we wish we may skip any instruction in the string T (possibly discarding all of them). You have to tell me how many di\ufb00erent nodes I can end up after following instruction string T (skipping as many instructions as I wish).<\/p>\r\n\r\n<p>For example:<\/p>\r\n\r\n<p>Suppose: S = L and T = LU. Our answer is 3. Following S we will end up at the left child of the root. Now, when we follow T, there may be 4 cases:<\/p>\r\n\r\n<ol>\r\n\t<li>Skipping all letters: we will be at the same node where we are.<\/li>\r\n\t<li>Skipping L and following U: we will be at the root.<\/li>\r\n\t<li>Following L and Skipping U: we will be at the left child of current node.<\/li>\r\n\t<li>Following both L and U: we will be at the same node as in case i.Since 3 di\ufb00erent nodes we can end up after following T, the answer is 3.<\/li>\r\n<\/ol>\r\n","input":"<p>First line of the test \ufb01le contains an integer N (&lt;= 15) denoting number of test cases. Hence follow N test cases. Each test case consists of two non empty strings. First line will contain instruction string S and the second line will contain the instruction string T. You may assume that there will not be any letter other than L, R or U in these strings. Length of the strings will not be greater than 100000.<\/p>\r\n","output":"<p>For each test case print the case number followed by the number of nodes we can end up \ufb01nally. Since the answer may be large, you have to give the answer modulo 21092013.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]