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문제

DNA 수열은 A, C, G, T로 이루어져 있다. DNA 수열의 GC-비율은 C와 G의 개수를 수열의 길이로 나눈 값이다. GC-비율이 높은 구간은 유전자의 시작 구간이 될 확률이 높다. 따라서, GC-비율은 매우 중요하다.

매우 긴 DNA 수열에서 수열의 모든 부분 수열 중에서 GC-비율이 가장 큰 부분 수열을 찾는 연구가 활발히 진행중이다. GC-비율이 높은 짧은 부분 수열은 의미없는 경우가 많기 때문에, 길이의 하한(lower bound)을 정해두고 부분 수열을 찾는다.

DNA 수열에서 모든 A와 T를 0으로, C와 G를 1로 바꿔서 길이가 같은 이진수열을 만들 수 있다. 이렇게 만든 이진수열의 평균값은 DNA 수열의 GC-비율과 같아진다.

인덱스 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
수열 0 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 0

이진수열이 위와 같이 주어을 때, 길이의 하한이 7이라면 평균이 최대인 부분 수열은 [7,14]가 되고, 평균은 6/8이다. 하한이 5인 경우, 평균이 최대인 부분 수열은 [7,11]이 되고, 평균은 4/5가 된다.

이진수열과 길이의 하한 L이 주어졌을 때, 길이가 적어도 L인 모든 부분 수열 중에서 평균이 최대인 부분 수열을 찾는 프로그램을 작성하시오. 같은 평균을 가지는 부분 수열이 여러 개인 경우, 길이가 짧은 것을 찾으면 된다. 길이가 짧은 것이 여러 개인 경우에는, 시작 위치가 앞서는 것을 찾는다.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스의 첫째 줄에는 이진수열의 길이 n(1 ≤ n ≤ 100,000)과 길이의 하한 L(1 ≤ L ≤ 1,000)이 주어진다. 다음 줄에는 길이가 n인 이진수열이 주어진다.

출력

각 테스트 케이스 마다 부분 수열의 시작 위치와 끝 위치를 출력한다. 

예제 입력 1

2
17 5
00101011011011010
20 4
11100111100111110000

예제 출력 1

7 11
6 9
[{"problem_id":"8925","problem_lang":"0","title":"GC-\ube44\uc728","description":"<p>DNA \uc218\uc5f4\uc740 A, C, G, T\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. DNA \uc218\uc5f4\uc758 GC-\ube44\uc728\uc740 C\uc640 G\uc758 \uac1c\uc218\ub97c \uc218\uc5f4\uc758 \uae38\uc774\ub85c \ub098\ub208 \uac12\uc774\ub2e4. GC-\ube44\uc728\uc774 \ub192\uc740 \uad6c\uac04\uc740 \uc720\uc804\uc790\uc758 \uc2dc\uc791 \uad6c\uac04\uc774 \ub420 \ud655\ub960\uc774 \ub192\ub2e4. \ub530\ub77c\uc11c, GC-\ube44\uc728\uc740 \ub9e4\uc6b0 \uc911\uc694\ud558\ub2e4.<\/p>\r\n\r\n<p>\ub9e4\uc6b0 \uae34 DNA \uc218\uc5f4\uc5d0\uc11c \uc218\uc5f4\uc758 \ubaa8\ub4e0 \ubd80\ubd84 \uc218\uc5f4 \uc911\uc5d0\uc11c GC-\ube44\uc728\uc774 \uac00\uc7a5 \ud070 \ubd80\ubd84 \uc218\uc5f4\uc744 \ucc3e\ub294 \uc5f0\uad6c\uac00 \ud65c\ubc1c\ud788 \uc9c4\ud589\uc911\uc774\ub2e4. GC-\ube44\uc728\uc774 \ub192\uc740 \uc9e7\uc740 \ubd80\ubd84 \uc218\uc5f4\uc740 \uc758\ubbf8\uc5c6\ub294 \uacbd\uc6b0\uac00 \ub9ce\uae30 \ub54c\ubb38\uc5d0, \uae38\uc774\uc758 \ud558\ud55c(lower bound)\uc744 \uc815\ud574\ub450\uace0 \ubd80\ubd84 \uc218\uc5f4\uc744 \ucc3e\ub294\ub2e4.<\/p>\r\n\r\n<p>DNA \uc218\uc5f4\uc5d0\uc11c \ubaa8\ub4e0 A\uc640 T\ub97c 0\uc73c\ub85c, C\uc640 G\ub97c 1\ub85c \ubc14\uafd4\uc11c \uae38\uc774\uac00 \uac19\uc740 \uc774\uc9c4\uc218\uc5f4\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub2e4. \uc774\ub807\uac8c \ub9cc\ub4e0 \uc774\uc9c4\uc218\uc5f4\uc758 \ud3c9\uade0\uac12\uc740 DNA \uc218\uc5f4\uc758 GC-\ube44\uc728\uacfc \uac19\uc544\uc9c4\ub2e4.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:100%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>\uc778\ub371\uc2a4<\/th>\r\n\t\t\t<th>1<\/th>\r\n\t\t\t<th>2<\/th>\r\n\t\t\t<th>3<\/th>\r\n\t\t\t<th>4<\/th>\r\n\t\t\t<th>5<\/th>\r\n\t\t\t<th>6<\/th>\r\n\t\t\t<th>7<\/th>\r\n\t\t\t<th>8<\/th>\r\n\t\t\t<th>9<\/th>\r\n\t\t\t<th>10<\/th>\r\n\t\t\t<th>11<\/th>\r\n\t\t\t<th>12<\/th>\r\n\t\t\t<th>13<\/th>\r\n\t\t\t<th>14<\/th>\r\n\t\t\t<th>15<\/th>\r\n\t\t\t<th>16<\/th>\r\n\t\t\t<th>17<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<th>\uc218\uc5f4<\/th>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>\uc774\uc9c4\uc218\uc5f4\uc774 \uc704\uc640 \uac19\uc774 \uc8fc\uc5b4\uc744 \ub54c, \uae38\uc774\uc758 \ud558\ud55c\uc774 7\uc774\ub77c\uba74 \ud3c9\uade0\uc774 \ucd5c\ub300\uc778 \ubd80\ubd84 \uc218\uc5f4\uc740 [7,14]\uac00 \ub418\uace0, \ud3c9\uade0\uc740 6\/8\uc774\ub2e4. \ud558\ud55c\uc774 5\uc778 \uacbd\uc6b0, \ud3c9\uade0\uc774 \ucd5c\ub300\uc778 \ubd80\ubd84 \uc218\uc5f4\uc740 [7,11]\uc774 \ub418\uace0, \ud3c9\uade0\uc740 4\/5\uac00 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc9c4\uc218\uc5f4\uacfc \uae38\uc774\uc758 \ud558\ud55c L\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uae38\uc774\uac00 \uc801\uc5b4\ub3c4 L\uc778 \ubaa8\ub4e0 \ubd80\ubd84 \uc218\uc5f4 \uc911\uc5d0\uc11c \ud3c9\uade0\uc774 \ucd5c\ub300\uc778 \ubd80\ubd84 \uc218\uc5f4\uc744 \ucc3e\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uac19\uc740 \ud3c9\uade0\uc744 \uac00\uc9c0\ub294 \ubd80\ubd84 \uc218\uc5f4\uc774 \uc5ec\ub7ec \uac1c\uc778 \uacbd\uc6b0, \uae38\uc774\uac00 \uc9e7\uc740 \uac83\uc744 \ucc3e\uc73c\uba74 \ub41c\ub2e4. \uae38\uc774\uac00 \uc9e7\uc740 \uac83\uc774 \uc5ec\ub7ec \uac1c\uc778 \uacbd\uc6b0\uc5d0\ub294, \uc2dc\uc791 \uc704\uce58\uac00 \uc55e\uc11c\ub294 \uac83\uc744 \ucc3e\ub294\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \uc774\uc9c4\uc218\uc5f4\uc758 \uae38\uc774 n(1 &le; n &le; 100,000)\uacfc \uae38\uc774\uc758 \ud558\ud55c L(1 &le; L &le; 1,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c \uc904\uc5d0\ub294 \uae38\uc774\uac00 n\uc778 \uc774\uc9c4\uc218\uc5f4\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub9c8\ub2e4 \ubd80\ubd84 \uc218\uc5f4\uc758 \uc2dc\uc791 \uc704\uce58\uc640 \ub05d \uc704\uce58\ub97c \ucd9c\ub825\ud55c\ub2e4.&nbsp;<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"8925","problem_lang":"1","title":"Average","description":"<p>A DNA sequence consists of four letters, A, C, G, and T. The GC-ratio of a DNA sequence is the number of Cs and Gs of the sequence divided by the length of the sequence. GC-ratio is important in gene finding because DNA sequences with relatively high GC-ratios might be good candidates for the starting parts of genes. Given a very long DNA sequence, researchers are usually interested in locating a subsequence whose GC-ratio is maximum over all subsequences of the sequence. Since short subsequences with high GC-ratios are sometimes meaningless in gene finding, a length lower bound is given to ensure that a long subsequence with high GC-ratio could be found. If, in a DNA sequence, a 0 is assigned to every A and T and a 1 to every C and G, the DNA sequence is transformed into a binary sequence of the same length. GC-ratios in the DNA sequence are now equivalent to averages in the binary sequence.&nbsp;<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:100%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>Position Index<\/th>\r\n\t\t\t<th>1<\/th>\r\n\t\t\t<th>2<\/th>\r\n\t\t\t<th>3<\/th>\r\n\t\t\t<th>4<\/th>\r\n\t\t\t<th>5<\/th>\r\n\t\t\t<th>6<\/th>\r\n\t\t\t<th>7<\/th>\r\n\t\t\t<th>8<\/th>\r\n\t\t\t<th>9<\/th>\r\n\t\t\t<th>10<\/th>\r\n\t\t\t<th>11<\/th>\r\n\t\t\t<th>12<\/th>\r\n\t\t\t<th>13<\/th>\r\n\t\t\t<th>14<\/th>\r\n\t\t\t<th>15<\/th>\r\n\t\t\t<th>16<\/th>\r\n\t\t\t<th>17<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<th>Sequence<\/th>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>For the binary sequence above, if the length lower bound is 7, the maximum average is 6\/8 which happens in the subsequence [7,14]. Its length is 8, which is greater than the length lower bound 7. If the length lower bound is 5, then the subsequence [7,11] gives the maximum average 4\/5. The length is 5 which is equal to the length lower bound. For the subsequence [7,11], 7 is its starting index and 11 is its ending index.&nbsp;<br \/>\r\n&nbsp;<br \/>\r\nGiven a binary sequence and a length lower bound L, write a program to find a subsequence of the binary sequence whose length is at least L and whose average is maximum over all subsequences of the binary sequence. If two or more subsequences have the maximum average, then find the shortest one; and if two or more shortest subsequences with the maximum average exist, then find the one with the smallest starting index.&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 a line containing two integers n (1&le;n&le;100,000) and L (1&le;L&le;1,000) which are the length of a binary sequence and a length lower bound, respectively. In the next line, a string, binary sequence, of length n is given.&nbsp;<\/p>\r\n","output":"<p>Your program is to write to standard output. Print the starting and ending index of the subsequence.&nbsp;<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Asia > Korea > Asia Regional - Seoul 2009 D번