시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

자카르타 시에는 N개의 큰 빌딩이 일직선 위에 위치하고 있다. 이들은 왼쪽부터 0, 1, ..., N - 1까지 번호가 붙어 있다. 자카르타에는 이들 말고 다른 큰빌딩은 없다.

자카르타에는 "도게"라고 불리는 신비한 생명체들이 살고 있다. 도게들은 0, 1, ..., M - 1 까지 번호가 붙어 있다. 도게 i는 최초에 빌딩 Bi에 위치하고 있다. 도게 i가 가진 신비한 힘은 그 능력치가 양의 정수 Pi로 표시된다. 도게는 이 신비한 힘으로 큰 빌딩들 간에 점프를 할 수 있다. 큰 빌딩 b에 있는 능력치가 p인 도게는 한번의 점프로 큰빌딩 b + p(0 ≤ b + p < N이라야 함) 혹은 큰빌딩 b - p(0 ≤ b - p < N이라야 함)로 이동할 수 있다.

도게 0이 가장 대단한 도게이며 모든 도게들의 지도자이다. 도게 0은 급한 소식이 있어 이 소식을 도게 1에게 전해야 한다. 물론 가장 빨리 소식이 전해지기를 바란다. 뉴스를 전해 들은 도게는 다음의 두가지 중 하나를 할 수 있다.

  • 다른 큰 빌딩으로 점프.
  • 현재 위치한 빌딩의 다른 도게에게 소식을 전달

도게들을 도와주는 프로그램을 작성해야 한다. 이 프로그램은 소식을 도게 1에게 전할 수 있는 최소한의 점프 횟수를 계산해야 한다. 만약 소식을 전달하는 것이 불가능한 경우라면 그것도 알아내야 한다.

입력

입력의 첫 줄에는 정수 NM이 주어진다. 이후 M개의 줄에는 두 자연수 BiPi가 주어진다.

  • 0 ≤ Bi < N
  • 1 ≤ N ≤ 30, 000
  • 1 ≤ Pi ≤ 30, 000
  • 2 ≤ M ≤ 30, 000

출력

출력은 단 한 줄이며, 최소의 점프 횟수라야 한다. 불가능한 경우 -1을 출력한다.

예제 입력 1

5 3
0 2
1 1
4 1

예제 출력 1

5

힌트

다음 경우가 5 번의 점프로 가능한 시나리오이다.

  • 도게 0이 큰빌딩 2로 점프, 또 큰빌딩 4로 점프 (2번 점프).
  • 도게 0이 소식을 도게 2에게 전함.
  • 도게 2가 큰빌딩 3으로 점프, 또 큰빌딩 2로 점프, 또 큰빌딩 1로 점프 (3번 점프).
  • 도게 2가 도게 1에게 소식을 전함.
[{"problem_id":"10847","problem_lang":"0","title":"\uc790\uce74\ub974\ud0c0\uc758 \ub9c8\ucc9c\ub8e8","description":"<p>\uc790\uce74\ub974\ud0c0 \uc2dc\uc5d0\ub294 <em>N<\/em>\uac1c\uc758 \ud070 \ube4c\ub529\uc774 \uc77c\uc9c1\uc120 \uc704\uc5d0 \uc704\uce58\ud558\uace0 \uc788\ub2e4. \uc774\ub4e4\uc740 \uc67c\ucabd\ubd80\ud130 0, 1, ..., <em>N<\/em> - 1\uae4c\uc9c0 \ubc88\ud638\uac00 \ubd99\uc5b4 \uc788\ub2e4. \uc790\uce74\ub974\ud0c0\uc5d0\ub294 \uc774\ub4e4 \ub9d0\uace0 \ub2e4\ub978 \ud070\ube4c\ub529\uc740 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uc790\uce74\ub974\ud0c0\uc5d0\ub294 &quot;\ub3c4\uac8c&quot;\ub77c\uace0 \ubd88\ub9ac\ub294 \uc2e0\ube44\ud55c \uc0dd\uba85\uccb4\ub4e4\uc774 \uc0b4\uace0 \uc788\ub2e4. \ub3c4\uac8c\ub4e4\uc740 0, 1, ..., <em>M<\/em> - 1 \uae4c\uc9c0 \ubc88\ud638\uac00 \ubd99\uc5b4 \uc788\ub2e4. \ub3c4\uac8c <em>i<\/em>\ub294 \ucd5c\ucd08\uc5d0 \ube4c\ub529 <em>B<\/em><sub><em>i<\/em><\/sub>\uc5d0 \uc704\uce58\ud558\uace0 \uc788\ub2e4. \ub3c4\uac8c <em>i<\/em>\uac00 \uac00\uc9c4 \uc2e0\ube44\ud55c \ud798\uc740 \uadf8 \ub2a5\ub825\uce58\uac00 \uc591\uc758 \uc815\uc218 <em>P<\/em><sub><em>i<\/em><\/sub>\ub85c \ud45c\uc2dc\ub41c\ub2e4. \ub3c4\uac8c\ub294 \uc774 \uc2e0\ube44\ud55c \ud798\uc73c\ub85c \ud070 \ube4c\ub529\ub4e4 \uac04\uc5d0 \uc810\ud504\ub97c \ud560 \uc218 \uc788\ub2e4. \ud070 \ube4c\ub529 <em>b<\/em>\uc5d0 \uc788\ub294 \ub2a5\ub825\uce58\uac00 <em>p<\/em>\uc778 \ub3c4\uac8c\ub294 \ud55c\ubc88\uc758 \uc810\ud504\ub85c \ud070\ube4c\ub529 <em>b<\/em> + <em>p<\/em>(0 &le; <em>b<\/em> + <em>p<\/em> &lt; <em>N<\/em>\uc774\ub77c\uc57c \ud568) \ud639\uc740 \ud070\ube4c\ub529 <em>b<\/em> - <em>p<\/em>(0 &le; <em>b<\/em> - <em>p<\/em> &lt; <em>N<\/em>\uc774\ub77c\uc57c \ud568)\ub85c \uc774\ub3d9\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub3c4\uac8c 0\uc774 \uac00\uc7a5 \ub300\ub2e8\ud55c \ub3c4\uac8c\uc774\uba70 \ubaa8\ub4e0 \ub3c4\uac8c\ub4e4\uc758 \uc9c0\ub3c4\uc790\uc774\ub2e4. \ub3c4\uac8c 0\uc740 \uae09\ud55c \uc18c\uc2dd\uc774 \uc788\uc5b4 \uc774 \uc18c\uc2dd\uc744 \ub3c4\uac8c 1\uc5d0\uac8c \uc804\ud574\uc57c \ud55c\ub2e4. \ubb3c\ub860 \uac00\uc7a5 \ube68\ub9ac \uc18c\uc2dd\uc774 \uc804\ud574\uc9c0\uae30\ub97c \ubc14\ub780\ub2e4. \ub274\uc2a4\ub97c \uc804\ud574 \ub4e4\uc740 \ub3c4\uac8c\ub294 \ub2e4\uc74c\uc758 \ub450\uac00\uc9c0 \uc911 \ud558\ub098\ub97c \ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ub2e4\ub978 \ud070 \ube4c\ub529\uc73c\ub85c \uc810\ud504.<\/li>\r\n\t<li>\ud604\uc7ac \uc704\uce58\ud55c \ube4c\ub529\uc758 \ub2e4\ub978 \ub3c4\uac8c\uc5d0\uac8c \uc18c\uc2dd\uc744 \uc804\ub2ec<\/li>\r\n<\/ul>\r\n\r\n<p>\ub3c4\uac8c\ub4e4\uc744 \ub3c4\uc640\uc8fc\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud574\uc57c \ud55c\ub2e4. \uc774 \ud504\ub85c\uadf8\ub7a8\uc740 \uc18c\uc2dd\uc744 \ub3c4\uac8c 1\uc5d0\uac8c \uc804\ud560 \uc218 \uc788\ub294 \ucd5c\uc18c\ud55c\uc758 \uc810\ud504 \ud69f\uc218\ub97c \uacc4\uc0b0\ud574\uc57c \ud55c\ub2e4. \ub9cc\uc57d \uc18c\uc2dd\uc744 \uc804\ub2ec\ud558\ub294 \uac83\uc774 \ubd88\uac00\ub2a5\ud55c \uacbd\uc6b0\ub77c\uba74 \uadf8\uac83\ub3c4 \uc54c\uc544\ub0b4\uc57c \ud55c\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uccab \uc904\uc5d0\ub294 \uc815\uc218 <em>N<\/em>\uacfc <em>M<\/em>\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ud6c4 <em>M<\/em>\uac1c\uc758 \uc904\uc5d0\ub294 \ub450 \uc790\uc5f0\uc218 <em>B<\/em><sub><em>i<\/em><\/sub>\uc640 <em>P<\/em><sub><em>i<\/em><\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>0 &le; B<sub>i<\/sub> &lt; N<\/li>\r\n\t<li>1 &le; N &le; 30, 000<\/li>\r\n\t<li>1 &le; P<sub>i<\/sub> &le; 30, 000<\/li>\r\n\t<li>2 &le; M &le; 30, 000<\/li>\r\n<\/ul>\r\n","output":"<p>\ucd9c\ub825\uc740 \ub2e8 \ud55c \uc904\uc774\uba70, \ucd5c\uc18c\uc758 \uc810\ud504 \ud69f\uc218\ub77c\uc57c \ud55c\ub2e4. \ubd88\uac00\ub2a5\ud55c \uacbd\uc6b0 -1\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\ub2e4\uc74c \uacbd\uc6b0\uac00 5 \ubc88\uc758 \uc810\ud504\ub85c \uac00\ub2a5\ud55c \uc2dc\ub098\ub9ac\uc624\uc774\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ub3c4\uac8c 0\uc774 \ud070\ube4c\ub529 2\ub85c \uc810\ud504, \ub610 \ud070\ube4c\ub529 4\ub85c \uc810\ud504 (2\ubc88 \uc810\ud504).<\/li>\r\n\t<li>\ub3c4\uac8c 0\uc774 \uc18c\uc2dd\uc744 \ub3c4\uac8c 2\uc5d0\uac8c \uc804\ud568.<\/li>\r\n\t<li>\ub3c4\uac8c 2\uac00 \ud070\ube4c\ub529 3\uc73c\ub85c \uc810\ud504, \ub610 \ud070\ube4c\ub529 2\ub85c \uc810\ud504, \ub610 \ud070\ube4c\ub529 1\ub85c \uc810\ud504 (3\ubc88 \uc810\ud504).<\/li>\r\n\t<li>\ub3c4\uac8c 2\uac00 \ub3c4\uac8c 1\uc5d0\uac8c \uc18c\uc2dd\uc744 \uc804\ud568.<\/li>\r\n<\/ul>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"10847","problem_lang":"1","title":"Jakarta Skyscrapers","description":"<p>The city of Jakarta has N skyscrapers located on a line, conveniently numbered 0 through N-1 from left to right. There are no other skyscrapers in Jakarta.<\/p>\r\n\r\n<p>Jakarta is inhabited by M mystical creatures called &rdquo;doge&rdquo;s. The doges are conveniently numbered 0 through M-1. Doge i initially resides in skyscraper B<sub>i<\/sub>. Doge i has a mystical power, represented with a positive integer P<sub>i<\/sub>. This mystical power enables doges to jump between skyscrapers. In a single jump, a doge with superpower p that is currently in skyscraper b can move to either skyscraper b+p (if 0 &le; b + p &lt; N) or skyscraper b-p (if 0 &le; b &minus; p &lt; N).<\/p>\r\n\r\n<p>Doge 0 is the most awesome doge, and it is the leader of all the doges. It has an urgent news for doge 1, and wants the news to reach doge 1 as quickly as possible. Any doge that has received the news can do any of the following actions:<\/p>\r\n\r\n<ul>\r\n\t<li>Make a jump to move to some other skyscraper.<\/li>\r\n\t<li>Pass the news to another doge in the same skyscraper.<\/li>\r\n<\/ul>\r\n\r\n<p>Please help the doges by calculating the minimum number of total jumps required by all doges to pass the news to doge 1, or if it is impossible to do so.<\/p>\r\n","input":"<p>The first line contains two integers N and M. Each of the next M lines contains two integers B<sub>i<\/sub> and P<sub>i<\/sub>.<\/p>\r\n\r\n<ul>\r\n\t<li>0 &le; B<sub>i<\/sub> &lt; N<\/li>\r\n\t<li>1 &le; N &le; 30, 000<\/li>\r\n\t<li>1 &le; P<sub>i<\/sub> &le; 30, 000<\/li>\r\n\t<li>2 &le; M &le; 30, 000<\/li>\r\n<\/ul>\r\n","output":"<p>A single line containing the minimum number of total jumps, or -1 if it is impossible.<\/p>\r\n","hint":"<p>Here is one of the possible scenarios to pass the news using 5 jumps:<\/p>\r\n\r\n<ul>\r\n\t<li>Doge 0 jumps to skyscraper 2 and then to skyscraper 4 (2 jumps).<\/li>\r\n\t<li>Doge 0 passes the news to doge 2.<\/li>\r\n\t<li>Doge 2 jumps to skyscraper 3, and then to skyscraper 2, and then to skyscraper 1 (3 jumps).<\/li>\r\n\t<li>Doge 2 passes the news to doge 1.<\/li>\r\n<\/ul>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]