시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 512 MB 199 46 35 28.000%

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 나머지로 새로운 수열 을 만들고, 그 수열의 각 자리 숫자로 새 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
[{"problem_id":"17840","problem_lang":"0","title":"\ud53c\ubcf4\ub098\uce58 \uc74c\uc545","description":"<p>\uc791\uace1\uac00 \ucca0\uc218\ub294 \ud53c\ubcf4\ub098\uce58 \uc218\uc5f4\uc744 \uc774\uc6a9\ud558\uc5ec \ub9cc\ub4e0 \ud53c\uc544\ub178 \uace1\uc744 \uc6b0\uc5f0\ud788 \uc720\ud29c\ube0c\uc5d0\uc11c \ubcf4\uac8c \ub418\uc5c8\ub2e4. \ud53c\ubcf4\ub098\uce58 \uc218\uc5f4\uc774\ub780 f<sub>1<\/sub> = 1, f<sub>2<\/sub> = 1, f<sub>n+2<\/sub> = f<sub>n+1<\/sub> + f<sub>n<\/sub> (\ubaa8\ub4e0 n &ge; 1\uc5d0 \ub300\ud574)\uc744 \ub9cc\uc871\ud558\ub294 \uc218\uc5f4\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc774 \uace1\uc740 \ud53c\ubcf4\ub098\uce58 \uc218\uc5f4\uc758 \uac01 \uc790\ub9ac \uc22b\uc790\uc5d0 \ud574\ub2f9\ud558\ub294 \uac74\ubc18\uc744 \ub20c\ub7ec\uc11c \ub9cc\ub4e4\uc5b4\uc84c\ub2e4.<br \/>\r\n\ud53c\ubcf4\ub098\uce58 \uc218\uc5f4\uc758 \uccab 8\uac1c \ud56d\uc744 \uc0ac\uc6a9\ud574 \uace1\uc744 \ub9cc\ub4e0\ub2e4\uba74, \ub2e4\uc74c\uacfc \uac19\uc774 \uac74\ubc18\uc744 \ucd1d 10\ubc88 \ub204\ub974\uac8c \ub420 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\">1 &rarr; 1 &rarr; 2 &rarr; 3 &rarr; 5 &rarr; 8 &rarr; 1 &rarr; 3 &rarr; 2 &rarr; 1<\/p>\r\n\r\n<p>\ucca0\uc218\ub294 \uc790\uc2e0\ub3c4 \uc774 \ubc29\ubc95\uc744 \uc0ac\uc6a9\ud574 \ubcf4\uae30\ub85c \ub9c8\uc74c\uba39\uc5c8\ub2e4. \uadf8\ub7f0\ub370 \ud53c\ubcf4\ub098\uce58 \uc218\uc5f4\uc740 \ub108\ubb34 \ube60\ub974\uac8c \uc99d\uac00\ud574\uc11c, \ub367\uc148\uc5d0 \uc57d\ud55c \ucca0\uc218\uac00 \uacc4\uc0b0\ud558\uae30\uc5d0\ub294 \uc5b4\ub824\uc6e0\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub798\uc11c \ucca0\uc218\ub294 \ubc29\ubc95\uc744 \uc870\uae08 \ubc14\uafb8\uae30\ub85c \ud588\ub2e4. \ucca0\uc218\ub294 \uc5b4\ub5a4 \uc218 M\uc744 \uc815\ud55c \ud6c4, \ud53c\ubcf4\ub098\uce58 \uc218\uc5f4\uc758 \uac01 \ud56d\uc744 M\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub85c <em>\uc0c8\ub85c\uc6b4 \uc218\uc5f4<\/em> \uc744 \ub9cc\ub4e4\uace0, \uadf8 \uc218\uc5f4\uc758 \uac01 \uc790\ub9ac \uc22b\uc790\ub85c \uc0c8 \ud53c\uc544\ub178 \uace1\uc744 \uc4f0\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4 M=10\uc77c \ub54c, <em>\uc0c8\ub85c\uc6b4 \uc218\uc5f4&nbsp;<\/em>\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\">{1, 1, 2, 3, 5, 8, 3, 1, &hellip;}<\/p>\r\n\r\n<p>\ub530\ub77c\uc11c \ucca0\uc218\ub294 1 &rarr;1 &rarr; 2 &rarr; 3 &rarr; 5 &rarr; 8 &rarr; 3 &rarr; 1 &rarr; 4&nbsp;&rarr; &hellip; \uc21c\uc73c\ub85c \uac74\ubc18\uc744 \ub204\ub974\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc774\ub54c, \ucca0\uc218\ub294 \uc5b4\ub5a4 N\uc5d0 \ub300\ud574 N\ubc88\uc9f8\ub85c \ub204\ub974\uac8c \ub418\ub294 \uac74\ubc18\uc758 \ubc88\ud638(i.e. <em>\uc0c8\ub85c\uc6b4 \uc218\uc5f4&nbsp;<\/em>\uc758 N\ubc88\uc9f8 \ud56d)\uac00 \uad81\uae08\ud574\uc84c\ub2e4.<\/p>\r\n\r\n<p>Q\uac1c\uc758 N\uc774 \uc9c8\uc758\ub85c&nbsp;\uc8fc\uc5b4\uc84c\uc744 \ub54c, \uac01\uac01\uc758 \uc9c8\uc758\uc5d0&nbsp;\ub300\ud574 N\ubc88\uc9f8\ub85c \ub204\ub974\uac8c \ub418\ub294 \uac74\ubc18\uc758 \ubc88\ud638\ub97c \ucd9c\ub825\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc5ec\ub77c.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \uc815\uc218 Q\uc640 M\uc774 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 Q\uac1c\uc758 \uc904\uc5d0 \uac01\uac01\uc758 \uc9c8\uc758\ub97c \ub098\ud0c0\ub0b4\ub294&nbsp;\uc815\uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 N\uc5d0 \ub300\ud574, N\ubc88\uc9f8\ub85c \ub204\ub974\uac8c \ub418\ub294 \uac74\ubc18\uc758 \ubc88\ud638(\uc0c8\ub85c\uc6b4 \uc218\uc5f4\uc758 <em>N<\/em>&nbsp;\ubc88\uc9f8 \ud56d)\ub97c \uc785\ub825\uc5d0 \uc8fc\uc5b4\uc9c4 \uc21c\uc11c\ub300\ub85c \ucd1d Q\uac1c\uc758 \uc904\uc5d0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\ud55c\uad6d\uc5b4","limit":"<ul>\r\n\t<li>1 &le; N &le;&nbsp;10<sup>15<\/sup><\/li>\r\n\t<li>2 &le; M &le; 1,000<\/li>\r\n\t<li>1 &le; Q &le; 100,000&nbsp;<\/li>\r\n<\/ul>\r\n"},{"problem_id":"17840","problem_lang":"1","title":"Fibonacci song","description":"<p>Elsa, a composer, happened to listen a piano song made using the Fibonacci sequence. Fibonacci sequence {f<sub>n<\/sub>} is defined by following recurrence relation:<\/p>\r\n\r\n<ul>\r\n\t<li>f<sub>1<\/sub>&nbsp;= 1,&nbsp;f<sub>2<\/sub>&nbsp;= 1,<\/li>\r\n\t<li>and for every n&nbsp;&ge; 1,&nbsp;f<sub>n+2<\/sub>&nbsp;= f<sub>n+1<\/sub>&nbsp;+ f<sub>n<\/sub>.<\/li>\r\n<\/ul>\r\n\r\n<p>The song was made by pressing the keys corresponding&nbsp;to each digit in the Fibonacci sequence. If you use the first eight entries of the Fibonacci sequence to make a song, you will press the 10 keys in total, as below.<\/p>\r\n\r\n<p style=\"text-align: center;\">1 &rarr; 1 &rarr; 2 &rarr; 3 &rarr; 5 &rarr; 8 &rarr; 1 &rarr; 3 &rarr; 2 &rarr; 1<\/p>\r\n\r\n<p>Elsa tried&nbsp;to compose piano song using this method.&nbsp;The Fibonacci sequence, however, increased so quickly that it was difficult to calculate.<\/p>\r\n\r\n<p>So Elsa&nbsp;decided to change the method a little. She created a new sequence with the remainder of the Fibonacci sequence, divided by some positive integer M. She&#39;s going to compose a new piano song using each digit of the new sequence.<\/p>\r\n\r\n<p>For example, if M = 10, new sequence is:<\/p>\r\n\r\n<p style=\"text-align: center;\">{1, 1, 2, 3, 5, 8, 3, 1, ...},<\/p>\r\n\r\n<p>therefore, she&nbsp;will press key in order of&nbsp;1 &rarr; 1 &rarr; 2 &rarr; 3 &rarr; 5 &rarr; 8 &rarr; 3 &rarr; 1 &rarr; 4&nbsp;&rarr; &hellip; .<\/p>\r\n\r\n<p>For fixed M, she wants to deal with following query:<\/p>\r\n\r\n<ul>\r\n\t<li>for given N, print N-th entry of the new sequence.<\/li>\r\n<\/ul>\r\n\r\n<p>She needs your help to deal with queries. Write a program that deals with queries.<\/p>\r\n","input":"<p>In the first line, two integers Q and M are given. Q is the number of queries.<\/p>\r\n\r\n<p>In each of following Q lines, an integer N, representing the query is given.<\/p>\r\n","output":"<p>For each 1&nbsp;&le; i&nbsp;&le; N, in the&nbsp;i-th line, output the answer of the i-th query. Note that the answer of the query is N-th entry of new sequence, where N is the integer given as input of query.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\uc601\uc5b4","limit":"<ul>\r\n\t<li>2&nbsp;&le; M&nbsp;&le; 1,000<\/li>\r\n\t<li>1&nbsp;&le; N&nbsp;&le; 10<sup>15<\/sup><\/li>\r\n\t<li>1&nbsp;&le; Q&nbsp;&le; 100,000<\/li>\r\n<\/ul>\r\n"}]