시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 256 MB4871198125.077%

문제

사람의 손가락은 10개이다. 따라서, 우리가 사용하는 숫자 체계는 10진법이다. 257이 의미하는 것은 2×102 + 5×101 + 7×100이다. 십진법의 각 자리는 0...9 구간에 포함된다.

10진법 말고 주로 사용하는 진법은 2진법, 8진법, 16진법이다. 이 진법은 컴퓨터에서 사용하거나, 다른 사람에게 큰 인상을 주기 위해서 사용한다. b진법의 각 자리는 0...b-1 구간에 포함된다. 또 각 자리를 오른쪽부터 읽었을 때, 곱해야 하는 수는 b의 다음 제곱이다.

예를 들어, 10진법에서 9는 다음과 같이 작성할 수 있다.

16진법으로는 9

8진법으로는 11 (1×81 + 1×80 = 9)

2진법으로는 1001 (1×23 + 0×22 + 0×21 + 1×20 = 9)

9는 위의 세가지 진법에서 모두 팰린드롬이다. 팰린드롬이란, 순서를 반대로 했을 때, 원래 순서와 같은 수열을 의미한다. 영단어에서 팰린드롬은 "dad", "mom", "racecar"가 있다. 9, 11, 1001과 같은 숫자도 팰린드롬이다.

10진법 숫자 X가 주어졌을 때, b진법으로 나타냈을 때, 팰린드롬인 것의 개수를 구하는 프로그램을 작성하시오. (2 ≤ b < X)

입력

첫째 줄에 X가 주어진다. (2 ≤ X ≤ 1,000,000,000)

출력

X를 b진법으로 나타냈을 때, 팰린드롬인 것을 모두 한 줄에 하나씩 증가하는 순서대로 출력한다.

예제 입력 1

9

예제 출력 1

2
8
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

출처

Olympiad > Canadian Computing Competition & Olympiad > 2013 > CCO 2013 1번

  • 잘못된 데이터를 찾은 사람: august14
  • 문제를 번역한 사람: baekjoon