시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 12 10 9 81.818%

문제

프로 드링커 상근이는 술을 마실때, 조세퍼스 문제와 같은 순서로 술을 마신다. 조세퍼스 문제를 천 번 넘게 푼 상근이는 머리 속으로 가장 마지막에 술을 마시는 사람의 위치를 계산할 수 있다. 따라서, 같이 술을 마시는 친구들은 상근이를 이기기 위해서 술을 마시는 새로운 순서를 제시했다.

먼저, 원탁에 모두 앉는다. 총 N명이 원탁에 앉았다면, 각 사람의 번호는 0번부터 N-1번이 된다.

조세퍼스 문제와 다르게 다음 사람을 고르기 위해서 두 숫자 a와 b를 이용한다. 현재 선택된 사람의 번호가 x라면, 다음 사람의 번호는 ax2+b mod N이 된다.

가장 처음 시작하는 사람의 번호는 0번이다. 다음 사람의 번호는 위의 식을 이용해서 고른다.

각 사람은 한 번의 기회를 더 받을 수 있다. 즉, 한 번 걸리면 술을 마시는 것이 아니고, 두 번 걸렸을 때, 술을 마시는 것이다.

만약, 어떤 사람이 세 번 걸렸다면, 그 즉시 모두 자리를 박차고 일어나 집으로 간다.

N과 a, b가 주어졌을 때, 술을 마시지 않고 집으로 가는 사람의 수를 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스는 한 줄로 이루어져 있으며, 세 숫자 N, a, b가 공백으로 구분되어져 있다. (2 ≤ N ≤ 109, 0 ≤ a, b < N) 또, 첫 사람이 술을 마시기 위해 필요한 단계의 수는 106보다 작다. 입력의 마지막 줄에는 0이 하나 주어진다.

출력

각 테스트 케이스에 대해서, 술을 마시지 않고 집으로 가는 사람의 수를 출력한다.

예제 입력 1

2 1 1
5 1 1
10 3 7
101 9 2
698253463 1 181945480
1000000000 999999999 999999999
0

예제 출력 1

0
2
4
96
698177783
999999994

힌트

조세퍼스 문제는 1158번을 참고하면 된다.

[{"problem_id":"6523","problem_lang":"0","title":"\uc870\uc138\ud37c\uc2a4 \ud55c \ubc88 \ub354!","description":"<p>\ud504\ub85c \ub4dc\ub9c1\ucee4 \uc0c1\uadfc\uc774\ub294 \uc220\uc744 \ub9c8\uc2e4\ub54c, \uc870\uc138\ud37c\uc2a4 \ubb38\uc81c\uc640 \uac19\uc740 \uc21c\uc11c\ub85c \uc220\uc744 \ub9c8\uc2e0\ub2e4. \uc870\uc138\ud37c\uc2a4 \ubb38\uc81c\ub97c \ucc9c \ubc88 \ub118\uac8c \ud47c \uc0c1\uadfc\uc774\ub294 \uba38\ub9ac \uc18d\uc73c\ub85c \uac00\uc7a5 \ub9c8\uc9c0\ub9c9\uc5d0 \uc220\uc744 \ub9c8\uc2dc\ub294 \uc0ac\ub78c\uc758 \uc704\uce58\ub97c \uacc4\uc0b0\ud560 \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c, \uac19\uc774 \uc220\uc744 \ub9c8\uc2dc\ub294 \uce5c\uad6c\ub4e4\uc740 \uc0c1\uadfc\uc774\ub97c \uc774\uae30\uae30 \uc704\ud574\uc11c \uc220\uc744 \ub9c8\uc2dc\ub294 \uc0c8\ub85c\uc6b4 \uc21c\uc11c\ub97c \uc81c\uc2dc\ud588\ub2e4.<\/p>\r\n\r\n<p>\uba3c\uc800, \uc6d0\ud0c1\uc5d0 \ubaa8\ub450 \uc549\ub294\ub2e4. \ucd1d N\uba85\uc774 \uc6d0\ud0c1\uc5d0 \uc549\uc558\ub2e4\uba74, \uac01 \uc0ac\ub78c\uc758 \ubc88\ud638\ub294 0\ubc88\ubd80\ud130 N-1\ubc88\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc870\uc138\ud37c\uc2a4 \ubb38\uc81c\uc640 \ub2e4\ub974\uac8c \ub2e4\uc74c \uc0ac\ub78c\uc744 \uace0\ub974\uae30 \uc704\ud574\uc11c \ub450 \uc22b\uc790 a\uc640 b\ub97c \uc774\uc6a9\ud55c\ub2e4. \ud604\uc7ac \uc120\ud0dd\ub41c \uc0ac\ub78c\uc758 \ubc88\ud638\uac00 x\ub77c\uba74, \ub2e4\uc74c \uc0ac\ub78c\uc758 \ubc88\ud638\ub294 ax<sup>2<\/sup>+b mod N\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uac00\uc7a5 \ucc98\uc74c \uc2dc\uc791\ud558\ub294 \uc0ac\ub78c\uc758 \ubc88\ud638\ub294 0\ubc88\uc774\ub2e4. \ub2e4\uc74c \uc0ac\ub78c\uc758 \ubc88\ud638\ub294 \uc704\uc758 \uc2dd\uc744 \uc774\uc6a9\ud574\uc11c \uace0\ub978\ub2e4.<\/p>\r\n\r\n<p>\uac01 \uc0ac\ub78c\uc740 \ud55c \ubc88\uc758 \uae30\ud68c\ub97c \ub354 \ubc1b\uc744 \uc218 \uc788\ub2e4. \uc989, \ud55c \ubc88 \uac78\ub9ac\uba74 \uc220\uc744 \ub9c8\uc2dc\ub294 \uac83\uc774 \uc544\ub2c8\uace0, \ub450 \ubc88 \uac78\ub838\uc744 \ub54c, \uc220\uc744 \ub9c8\uc2dc\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc57d, \uc5b4\ub5a4 \uc0ac\ub78c\uc774 \uc138 \ubc88 \uac78\ub838\ub2e4\uba74, \uadf8 \uc989\uc2dc \ubaa8\ub450 \uc790\ub9ac\ub97c \ubc15\ucc28\uace0 \uc77c\uc5b4\ub098 \uc9d1\uc73c\ub85c \uac04\ub2e4.<\/p>\r\n\r\n<p>N\uacfc a, b\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc220\uc744 \ub9c8\uc2dc\uc9c0 \uc54a\uace0 \uc9d1\uc73c\ub85c \uac00\ub294 \uc0ac\ub78c\uc758 \uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud55c \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, \uc138 \uc22b\uc790 N, a, b\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4\uc838 \uc788\ub2e4. (2 &le; N &le; 10<sup>9<\/sup>, 0 &le; a, b &lt; N) \ub610, \uccab \uc0ac\ub78c\uc774 \uc220\uc744 \ub9c8\uc2dc\uae30 \uc704\ud574 \ud544\uc694\ud55c \ub2e8\uacc4\uc758 \uc218\ub294 10<sup>6<\/sup>\ubcf4\ub2e4 \uc791\ub2e4. \uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ud558\ub098 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \uc220\uc744 \ub9c8\uc2dc\uc9c0 \uc54a\uace0 \uc9d1\uc73c\ub85c \uac00\ub294 \uc0ac\ub78c\uc758 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc870\uc138\ud37c\uc2a4 \ubb38\uc81c\ub294&nbsp;<a href=\"http:\/\/www.acmicpc.net\/problem\/1158\">1158\ubc88<\/a>\uc744&nbsp;\ucc38\uace0\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"6523","problem_lang":"1","title":"Flavius Josephus Reloaded","description":"<p>Flavius Josephus once was trapped in a cave together with his comrade soldiers surrounded by Romans. All of Josephus&#39; fellow soldiers preferred not to surrender but to commit suicide. So they all formed a circle and agreed on a number k. Every k-th person in the circle would then commit suicide. However, Josephus had different priorities and didn&#39;t want to die just yet. According to the legend he managed to find the safe spot in the circle where he would be the last one to commit suicide. He surrendered to the Romans and became a citizen of Rome a few years later.<\/p>\r\n\r\n<p>It is a lesser known fact that the souls of Josephus and his comrades were all born again in modern times. Obviously Josephus and his reborn fellow soldiers wanted to avoid a similar fiasco in the future. Thus they asked a consulting company to work out a better decision scheme. The company came up with the following scheme:<\/p>\r\n\r\n<ul>\r\n\t<li>For the sake of tradition all soldiers should stand in a circle. This way a number between 0 and N-1 is assigned to each soldier, where N is the number of soldiers.<\/li>\r\n\t<li>As changing numbers in the old scheme turned out to be horribly inefficient, the number assigned to a soldier will not change throughout the game.<\/li>\r\n\t<li>The consulting company will provide two numbers a and b which will be used to calculate the number of the next soldier as follows: Let x be the number of the current soldier, then the number of the next soldier is the remainder of a&middot;x2 + b mod N.<\/li>\r\n\t<li>We start with the soldier with number 0 and each soldier calculates the number of the next soldier according to the formula above.<\/li>\r\n\t<li>As everyone deserves a second chance a soldier will commit suicide once his number is calculated for the second time.<\/li>\r\n\t<li>In the event that the number of a soldier is calculated for the third time the game will end and all remaining soldiers will surrender.<\/li>\r\n<\/ul>\r\n\r\n<p>You are to write a program that given the number of soldiers N and the constants a and b determines the number of survivors<\/p>\r\n","input":"<p>The input file consists of several test cases. Each test case consists of a single line containing the three integers N (2 &le; N &le; 10<sup>9<\/sup>), a and b (0 &le; a,b &lt; N) separated by white space. You may safely assume that the first soldier dies after no more than one million (10<sup>6<\/sup>) steps. The input is terminated by a single number 0 which should not be processed<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","output":"<p>For each test case output a single line containing the number of soldiers that survive.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]