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문제

과외맨은 배트맨, 스파이더맨, 슈퍼맨과 같은 슈퍼 히어로를 따라하는 한국의 대표 영웅이다. 오늘은 스파이더맨을 따라해보려고 한다. 과외맨은 고층 건물의 옥상을 점프하면서 돌아다니려고 한다.

고층 건물은 총 N개가 있고, 왼쪽에서 오른쪽으로 1번부터 N번까지 번호가 매겨져 있다. 지금 과외맨은 K번 건물 위에 있다. 과외맨은 아직 힘이 많이 부족한다. 따라서, 현재 있는 건물의 왼쪽 또는 오른쪽 건물로만 점프해서 이동할 수 있다. 또, 지금 자신이 있는 건물의 높이보다 높지 않은 빌딩으로만 이동할 수 있다.

이런 과외맨을 도와주고 위해서 상근이는 일부 건물의 옥상에 트램폴린을 설치해 놓았다. 과외맨이 트램폴린을 이용해 점프를 한다면 다른 모든 건물로 이동할 수 있고, 건물의 높이와 상관없이 이동할 수 있다.

과외맨이 방문할 수 있는 서로 다른 건물의 개수의 최댓값을 구하는 프로그램을 작성하시오. 과외맨은 점프를 K번 빌딩에서 시작한다. 같은 건물을 여러 번 방문할 때도, 방문한 건물의 개수는 한 개로 센다. 

입력

첫째 줄에 건물의 수 N과 점프를 시작하는 건물의 번호 K가 주어진다. (3 ≤ N ≤ 300,000, 1 ≤ K ≤ N)

둘째 줄에는 106보다 작은 N개의 정수가 주어진다. 이 정수는 건물의 높이이며, 1번 건물부터 순서대로 주어진다.

셋째 줄에는 '.' 또는 'T'로 이루어진 N개의 문자가 주어진다. i번째 문자가 'T'인 경우에는 i번 건물의 옥상에 트램폴린이 설치되어 있는 것이다.

출력

첫째 줄에 과외맨이 방문할 수 있는 서로 다른 건물 개수의 최댓값을 출력한다.

예제 입력 1

10 1
10 7 3 1 1 9 8 2 4 10
..T..T....

예제 출력 1

7

힌트

1 -> 2 -> 3 -> 6 -> 10 -> 9 -> 8

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(3 &le; N &le; 300,000, 1 &le; K &le; N)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 10<sup>6<\/sup>\ubcf4\ub2e4 \uc791\uc740 N\uac1c\uc758 \uc815\uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc815\uc218\ub294 \uac74\ubb3c\uc758 \ub192\uc774\uc774\uba70, 1\ubc88 \uac74\ubb3c\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc14b\uc9f8 \uc904\uc5d0\ub294 &#39;.&#39; \ub610\ub294 &#39;T&#39;\ub85c \uc774\ub8e8\uc5b4\uc9c4 N\uac1c\uc758 \ubb38\uc790\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. i\ubc88\uc9f8 \ubb38\uc790\uac00 &#39;T&#39;\uc778 \uacbd\uc6b0\uc5d0\ub294 i\ubc88 \uac74\ubb3c\uc758 \uc625\uc0c1\uc5d0 \ud2b8\ub7a8\ud3f4\ub9b0\uc774 \uc124\uce58\ub418\uc5b4 \uc788\ub294 \uac83\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uacfc\uc678\ub9e8\uc774 \ubc29\ubb38\ud560 \uc218 \uc788\ub294 \uc11c\ub85c \ub2e4\ub978 \uac74\ubb3c \uac1c\uc218\uc758 \ucd5c\ub313\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>1 -&gt; 2 -&gt; 3 -&gt; 6 -&gt; 10 -&gt; 9 -&gt; 8<\/p>\r\n\r\n<p><iframe frameborder=\"0\" height=\"480\" src=\"http:\/\/www.youtube.com\/embed\/_uYx13TPm-A\" width=\"853\"><\/iframe><\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2797","problem_lang":"1","title":"TRAMPOLIN","description":"<p>There are many action superheroes out there: Batman, Spiderman, Superman, Icantwriteman etc. Among them, there is one gentleman called Kickass. Today he wants to mimic Spiderman, so he has chosen a row of tall skyscrapers to jump around on.<\/p>\r\n\r\n<p>Specifically, he has chosen a sequence of N skyscrapers numbered 1 through N from left to right. He is initially located on the Kth skyscraper. Unfortunately, Kickass has very limited powers, and can therefore jump only to the adjacent skyscraper to the left or right, and only if that skyscraper&#39;s height is not greater than the height of the skyscraper he is currently on. However, anticipating this and not wanting to look weak, he has positioned trampolines on top of some skyscrapers, and from these skyscrapers he can jump onto any other skyscraper, no matter how tall or where that skyscraper is.<\/p>\r\n\r\n<p>Find the maximum number of different skyscrapers Kickass can visit in a chain of jumps starting from the skyscraper numbered K. If a skyscraper is visited more than once, we still count it only once.&nbsp;<\/p>\r\n\r\n<p>Moreover, skyscraper K is counted even if we never return to it.<\/p>\r\n","input":"<p>The first line of input contains the two integers N and K (3 &le; N &le; 300 000, 1 &le; K &le; N), the total number of skyscrapers and the starting skyscraper, respectively.<\/p>\r\n\r\n<p>The second line of input contains N integers less than 10<sup>6<\/sup>, the heights of skyscrapers in order from left to right.<\/p>\r\n\r\n<p>The third line of input contains a sequence of N characters &#39;.&#39; or &#39;T&#39;. If the ith character is &#39;T&#39;, then there is a trampoline positioned on the top of skyscraper i.<\/p>\r\n","output":"<p>The first and only line of output must contain the required maximum number of visited skyscrapers.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"<p>the sequence of visited skyscrapers could be the following:&nbsp;<\/p>\r\n\r\n<p>1 -&gt; 2 -&gt; 3 -&gt; 6 -&gt; 10 -&gt; 9 -&gt; 8.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]