시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 512 MB109923916321.252%

문제

작곡가 철수는 피보나치 수열을 이용하여 만든 피아노 곡을 우연히 유튜브에서 보게 되었다. 피보나치 수열이란 f1 = 1, f2 = 1, fn+2 = fn+1 + fn (모든 n ≥ 1에 대해)을 만족하는 수열이다.

이 곡은 피보나치 수열의 각 자리 숫자에 해당하는 건반을 눌러서 만들어졌다. 피보나치 수열의 첫 8개 항을 사용해 곡을 만든다면, 다음과 같이 건반을 총 10번 누르게 될 것이다.

1 → 1 → 2 → 3 → 5 → 8 → 1 → 3 → 2 → 1

철수는 자신도 이 방법을 사용해 보기로 마음먹었다. 그런데 피보나치 수열은 너무 빠르게 증가해서, 덧셈에 약한 철수가 계산하기에는 어려웠다.

그래서 철수는 방법을 조금 바꾸기로 했다. 철수는 어떤 수 M을 정한 후, 피보나치 수열의 각 항을 M으로 나눈 나머지를 구하고, 각 수의 각 자리 숫자로 새로운 수열 을 만들어 이에 따라 피아노 곡을 쓰려고 한다.

예를 들어 M=10일 때, 새로운 수열 은 다음과 같다.

{1, 1, 2, 3, 5, 8, 3, 1, …}

따라서 철수는 1 →1 → 2 → 3 → 5 → 8 → 3 → 1 → 4 → … 순으로 건반을 누르게 된다.

이때, 철수는 어떤 N에 대해 N번째로 누르게 되는 건반의 번호(i.e. 새로운 수열 의 N번째 항)가 궁금해졌다.

Q개의 N이 질의로 주어졌을 때, 각각의 질의에 대해 N번째로 누르게 되는 건반의 번호를 출력하는 프로그램을 작성하여라.

입력

첫 번째 줄에는 정수 Q와 M이 공백을 사이에 두고 주어진다.

두 번째 줄부터 Q개의 줄에 각각의 질의를 나타내는 정수 N이 주어진다.

출력

각각의 N에 대해, N번째로 누르게 되는 건반의 번호(새로운 수열의 N 번째 항)를 입력에 주어진 순서대로 총 Q개의 줄에 출력한다.

제한

  • 1 ≤ N ≤ 1015
  • 2 ≤ M ≤ 1,000
  • 1 ≤ Q ≤ 100,000

예제 입력 1

2 10
5
8

예제 출력 1

5
1
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