시간 제한메모리 제한제출정답맞힌 사람정답 비율
3 초 (추가 시간 없음) 1024 MB (추가 메모리 없음)6996100.000%

문제

원형 게임판에 $N$개의 스프링이 있다. 스프링은 시계 방향으로 $1$번 부터 $N$번 까지 번호가 붙어 있다. 각 스프링은 빨간색 또는 파란색으로 칠해져 있는데, 빨간 스프링을 밟으면 바로 양옆에 있는 스프링으로 점프할 수 있으며 파란 스프링을 밟으면 양옆으로 두 칸 거리에 있는 스프링으로 점프할 수 있다.

그림 L.1: 두 로봇이 1번과 6번 스프링에 있고, 반시계 방향 점프 명령을 한 경우 로봇의 움직임

당신은 두 로봇을 이용하여 게임을 할 것이다. 우선 게임판에 두 로봇을 서로 다른 번호의 스프링 위에 놓는다. 당신은 로봇들에게 시계 방향 또는 반시계 방향으로 움직이라고 명령할 수 있다. 명령을 내리면 두 로봇이 동시에 당신이 명령한 방향으로 점프한다. 즉 로봇을 하나만 움직이거나 두 로봇이 다른 방향으로 점프하도록 할 수는 없다.

게임은 두 로봇이 서로 다른 색깔 스프링을 밟으면 끝난다. 로봇의 시작 위치가 주어지면 게임을 끝내기 위해 필요한 최소 명령 수를 구하여라.

입력

첫 번째 줄에 스프링의 수 $N$($ 3 \leq N \leq 100\ 000 $)과 질문의 수 $Q$($ 1 \leq Q \leq 100\ 000 $)가 주어진다.

두 번째 줄에 스프링의 종류가 $1$번 스프링부터 $N$번 스프링까지 순서대로 주어진다. 빨간 스프링은 $1$, 파란 스프링은 $2$이다.

세 번째 줄부터 $Q$개의 줄에는 두 로봇이 게임을 시작할 스프링의 번호 $R1$, $R2$가 주어진다. ($1 \leq R1, R2 \leq N$, $R1 \neq R2$)

출력

$Q$개의 줄에 걸쳐 두 로봇이 다른 색깔 스프링에 위치하기 위해 필요한 최소 명령 수를 출력한다. 처음부터 두 로봇이 다른 색깔 스프링에 있었으면 0을, 아무리 명령하더라도 두 로봇이 다른 색깔 스프링에 있게 할 수 없다면 -1을 출력한다.

예제 입력 1

8 3
1 2 2 2 1 2 1 2
1 2
1 5
3 6

예제 출력 1

0
-1
1
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($1 \\leq R1, R2 \\leq N$, $R1 \\neq R2$)<\/p>\r\n","output":"<p>$Q$\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 \ub450 \ub85c\ubd07\uc774 \ub2e4\ub978 \uc0c9\uae54 \uc2a4\ud504\ub9c1\uc5d0 \uc704\uce58\ud558\uae30 \uc704\ud574 \ud544\uc694\ud55c \ucd5c\uc18c \uba85\ub839 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \ucc98\uc74c\ubd80\ud130 \ub450 \ub85c\ubd07\uc774 \ub2e4\ub978 \uc0c9\uae54 \uc2a4\ud504\ub9c1\uc5d0 \uc788\uc5c8\uc73c\uba74 <code>0<\/code>\uc744, \uc544\ubb34\ub9ac \uba85\ub839\ud558\ub354\ub77c\ub3c4 \ub450 \ub85c\ubd07\uc774 \ub2e4\ub978 \uc0c9\uae54 \uc2a4\ud504\ub9c1\uc5d0 \uc788\uac8c \ud560 \uc218 \uc5c6\ub2e4\uba74 <code>-1<\/code>\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"22884","problem_lang":"1","title":"Make Different","description":"<p>There are&nbsp;$N$&nbsp;springs on a circular game board. There are two types of springs: red springs and blue springs. When the robot steps on a red spring, it can jump one spring left or right. When the robot steps on a blue spring, it can jump two springs left or right.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/292dfe6e-fc20-480d-8c86-d02dddc7a48c\/-\/preview\/\" style=\"width: 480px; height: 285px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\"><em>The case when the two robots are on springs 1 and 6 respectively, and a counterclockwise jump command is given.<\/em><\/p>\r\n\r\n<p>You will play a game using two robots. In the beginning, you will place the two robots on different springs on the board. You can then issue a direction - either clockwise or counterclockwise. Both robots will jump simultaneously in the direction you command. The game ends when the robots step on springs of different colors.<\/p>\r\n\r\n<p>You are given&nbsp;$Q$&nbsp;queries. Each query contains the starting springs of the two robots. For each query, find the minimum number of commands needed to finish the game.<\/p>\r\n","input":"<p>The first line contains two integers&nbsp;$N$&nbsp;and&nbsp;$Q$&nbsp;($3 \\leq N \\leq 100\\,000$,&nbsp;$1 \\leq Q \\leq 100\\,000 $).<\/p>\r\n\r\n<p>The next line contains&nbsp;$N$&nbsp;integers, the&nbsp;$i$-th integer denoting the type of spring&nbsp;$i$. Red springs are denoted by a&nbsp;$1$&nbsp;and blue springs are denoted by a&nbsp;$2$.<\/p>\r\n\r\n<p>The next&nbsp;$Q$&nbsp;lines each contain two integers&nbsp;$p_1$&nbsp;and&nbsp;$p_2$&nbsp;denoting the positions at which the two robots will start the game ($1 \\leq p_1, p_2 \\leq N$,&nbsp;$p_1 \\neq p_2$).<\/p>\r\n","output":"<p>Output&nbsp;$Q$&nbsp;lines. On the&nbsp;$i$-th line, output a single integer denoting the minimum number of commands required to get the two robots to land on different colored springs for the&nbsp;$i$-th query. If it is impossible to get the robots to land on different colored springs, output&nbsp;<code>-1<\/code>.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]